Voiceless sounds that are produced with supralaryngeal configurations that would be considered approximants if voiced are attested in languages (i.e. [j̊], [l̥], etc.), but none are found to contrast with homorganic fricatives ([ç], [ɬ], etc.).
There seems to be a discrepancy in literature between some phoneticians who claim that the sounds should be referred to as fricatives and that a voiceless approximant means no audible effect, and others who claim that they should be referred to as approximants and that a distinction can be drawn between voiceless fricatives and approximants on phonetic grounds.
For example, Akamatsu (1992: 30) said:
I will dismiss out of hand as simply wrong Ladefoged's reference to the second segment in [pr̥ei] pray, [tr̥ai] try or [kr̥ai] cry as a voiceless approximant. The second segment in question is a fricative (cf. Gimson 1989: 208), not an approximant. At any rate, a voiceless approximant should be silence, as O'Connor (1973: 61) rightly points out. [...] Abercrombie seems to exclude laterals from the category of approximants. [...] The view that a voiceless frictionless continuant would be silence seems to be shared, independently, by Arnold (1963: 4).
Catford apparently raised this issue in his 1977 Fundamental Problems in Phonetics. In his review, Ladefoged said:
C[atford] distinguishes approximants from resonants—another useful sharpening of terminology. He defines approximants as those sounds with strictures insufficient to cause turbulent air-flow (friction) when voiced, but with strictures sufficient to produce friction with the higher air-flow that occurs in a voiceless sound. Resonants involve strictures that would be insufficient to produce turbulent air-flow even when voiceless. This definition neatly separates [j w ɹ l] and really close versions of [i u] from most other vowel and vowel-like sounds. Its only weakness is that it would also include fully back versions of [o ɔ ɑ] among the approximants. [...] C's definition of the term 'approximant' is preferable to that given by Ladefoged 1975. (p. 905)
Ladefoged & Maddieson (1996: 198-9) said:
[T]here is a widespread tradition of regarding all voiceless laterals as fricatives, with turbulence necessarily resulting from the air passing through the lateral aperture (cf. Pike 1943). However, we draw a distinction between voiceless laterals that are articulated with an aperture comparable in area to that of voiced lateral approximants and those produced with a more constricted aperture, comparable to that of other fricatives. [...] Maddieson and Emmorey (1984) compared Burmese and Tibetan, which have voiceless lateral approximants, with Navajo and Zulu, which have voiceless lateral fricatives. Their measures showed that the voiceless approximants typically have a lower amplitude of noise, a greater tendency to anticipate the voicing of a following vowel, and a concentration of energy lower in the spectrum than voiceless fricative laterals do. [...] The distinction between Burmese and Tibetan as opposed to Navajo and Zulu is quite clear, but in other cases it is difficult to decide whether a voiceless lateral should be described as an approximant or a fricative.
The onset in [English hue] is normally a voiceless palatal approximant, j̥, for which the IPA has no unitary symbol. [...] [T]he voiceless counterpart of w cannot have friction at both the labial and velar places of articulation [...], so if it is a fricative, it is better described as a voiceless labialized velar fricative.
However, Peter Roach, who was IPA Secretary when Ladefoged was President, wrote on Wikipedia in 2012:
As the WP article on the subject says, an approximant involves an articulation that does not become close enough to generate noise. Therefore an approximant does not produce noise. If an approximant is voiceless, then there is no vocal fold vibration going on to produce audible sound. Therefore the [ʍ] as you classify it in your modified IPA chart is noiseless and voiceless, and therefore completely silent. [...]
I cannot conceive of any way in which the reduced resistance to air flow from the lungs in a voiceless segment could result in increased pulmonic pressure. It would, however, make sense to claim that the reduced resistance to air flow from the lungs results in a higher rate of air flow through the vocal tract. The passage quoted could then go on to say that as a result of this higher rate of flow, sounds which when voiced are approximants become voiceless fricatives.
John Wells wrote in 2009 taking a similar position:
One problem with classifying [h] as an approximant is that voiceless approximants are by definition inaudible. (Or by one definition, at least. Approximants used to be known as “frictionless continuants”.) If there’s no friction and no voicing, there’s nothing to hear. Anything you can hear during a voiceless [h] must be some sort of weak friction, resulting from some sort of weak turbulence, which means that [h] is some sort of weak fricative — but still a fricative.
In the Wikipedia discussion, Ohala (2005: 276) was quoted:
From these equations we see that turbulence can be increased by decreasing the crossdimensional area of the channel. This is the usual view of how fricatives differ from approximants. But I don't think this is what is involved in the cases cited. Rather, another way to create turbulence is by increasing U, the volume velocity and this, in turn, can be effected by increasing POral. In the case of [ɬ], the POral is increased by virtue of its voicelessness: this reduces the resistance at the glottis to the expiratory air flow. The upstream pressure is then essentially the higher pulmonic pressure. Thus the fricative character of the [ɬ] need not result from its having a narrower channel than the approximant [l] but simply from being [-voice].
Asu, Nolan & Schötz (2015) tackled the very present question via an acoustic analysis of voiceless laterals in three languages, and said:
Welsh showed no pre-voicing in the lateral, whilst Icelandic and Estonian Swedish did, though the latter less consistently. The Welsh voiceless lateral was also greater in relative intensity. This could be taken as a difference of phonetic category between a fricative [ɬ] in Welsh as against a voiceless approximant [l̥] in the other two languages, but we argue that the complexity of the data from Estonian Swedish excludes a categorical interpretation.
So which is the dominant view in phonetics, the one that posits voiceless approximants distinct from voiceless fricatives or the one that does not? And what about in phonology? Do the sounds mentioned at the beginning more often pattern with sonorants or with obstruents? The answers in Is there a voiced-unvoiced pair for R or L in any language? touch on this but I'd like to know the mainstream view in each field (if there is).
(I guess what I'm looking for most is whether a distinction between (what Ladefoged & Maddieson describe as) voiceless approximants and fricatives has been found useful by a majority of those who study cross-linguistic, phonologically-informed phonetics. For example, it is beyond dispute that a lateral can have either one or both sides of the tongue open, but phoneticians (and phonologists) rarely make a distinction between them because they don't contrast (and possibly also because it is difficult to find out via an easily accessible means), and I'm wondering if something along the same lines could be said about voiceless fricatives vs. approximants.)