I had an idea for a voiced fricative being an approximant. I tried to say a voiced h and I noticed how similar it was to the schwa vowel. I just want to know if this is a possible approximant sound.
[h], customarily referred to as a voiceless glottal fricative, in reality denotes any voiceless articulation with no interruption of the airflow in the oral cavity, with no defined configuration of the tongue or the lips. [ɦ] is the same except the vocal folds oscillate to some extent. So some argue they are best regarded as placeless consonants.
So if you try to produce [h] in isolation with the normal articulatory setting, the position of the tongue and lips probably resembles that when producing [ə], so that if you voice it you will be producing [ə].
The only difference between a vowel and an approximant is that the former constitutes the peak of a syllable, which is a distinction made in the domain of phonology rather than phonetics and is language-dependent. Approximants are typically articulated like high vowels, but approximant versions of lower vowels are also found, like [o̯] found in some varieties of Spanish in words like poeta, and [ə̯] found in non-rhotic varieties of English in words like here, though such sounds are more often referred to as non-syllabic vowels, glides or semivowels than as approximants.
[ɚ] found in rhotic varieties of English is essentially a syllabic version of [ɹ], making equivalent [ɚ] and [ɹ̩], and, conversely, [ɹ] and [ɚ̯].
A small cap H has been used by some structuralist phonemicists to stand for the centralizing glide which is very prominent in some American dialects. Perhaps someone who knows that literature better than I can tell us just where this got started, though I cannot, but my guess is that the basis for it is not any phonetic similarity between offset [H] and onset [h], but rather that they are in complementary distribution. As we will recall, this was once regarded as an important criterion for grouping allophones into one phoneme.
I don't think that, as a matter of fact, there is any significant phonetic similarity between the two.
As a phonetic term, approximants refer to a class of consonants which covers liquids and glides (which includes laryngeal glides), so a vowel is not an approximant. In the SPE feature tradition, vowels and glides have in common the property of being [–consonantal]. The most likely reason why it sounds to you like a schwa is that many consonants cannot be "satisfactorily" produced without a following vocoid which allows you to tell what the consonant is (obviously with /t/, also /d/). At least for English speakers, the most natural vocalic accompaniment is something like schwa. The tongue is in what's called "the neutral position", neither raised nor lowered, fronted or backed. That is probably why it seems to sound like schaw.