Some presuppositions of the question need to be exposed, mainly regarding the term "allophonic". The historical distinction between "allophonic" vs. "morphophonemic" has fallen into desuetude, to the point that it is rare to find any contemporary mention of "allophony" that accepts the idea that being allophonic (as opposed to something else) is an important and well-defined theoretical concept. Instead, the question is generally expressed in terms of whether a process is "phonetic" or "phonetic implementation", vs. "phonological".
In SPE theory, things that are typically called "allophonic" are simply (and by fiat) the result of phonological rules, and the term "phonetic" is reserved for unavoidable, physically mandated facts that are not in grammars. Unfortunately, there has been huge confusion in the literature over what kinds of things are "automatic". For example, vowel to vowel coarticulation is considered by some to be "automatic", probably because of the word "coarticulation" (since in the transition from an oral segment to a nasal segment, there is, necessarily, some transitional interval). But "vowel to vowel coarticulation" is just another term for "vowel harmony", which can be contrastive in some languages, and just allophonic in others.
Because of the huge uncertainty attached to the term "allophone", questions about whether a particular fact can be called allophonic is fundamentally unanswerable, unless you add a vast amount of theoretical context (e.g. "assuming Bloch's Postulates"). Sensible answers are possible if you ask whether a process is phonological vs. phonetic, and that does require you to accept that both things exist (SPE denies that there is such a thing as phonetics as we now understand it; Bob Port denies that there is such a thing as phonology; so you have to at least presuppose that "phonetics" and "phonology" are referring terms). I would especially tag the work of Abby Cohn as productively making that assumption, as well as work by Pat Keating and Nick Clements. Zsiga's paper in Language on Igbo likewise persuasively makes the distinction.
This brings us back to the wording of your question, referring to "this kind of variation" -- specifically making me ask which kind of variation. If we define "allophonic" as "phonological, but not contrastive in the language", then in the context of theories that distinguish phonetic and phonological, ZCR would not be phonological. I haven't ever looked at (even computed) ZCR, but simple visual inspection of waveforms indicates that zero-crossing can be quite volatile, to the point that it does not give way to yes/no categorization. If a property could be analyzed in terms of a small set of categories, then the property could be phonological, but if it is truly continuous (e.g. formant frequency, duration, amplitude, number of zero-crossings), then it can't be phonological.
Unfortunately, Mark Hale doesn't do acoustic phonetics, so his take on the matter is not coupled with a bunch of measurements that argue this, but he distinguishes numerous "outputs", which includes not just the acoustic wave detected remotely, but also the physical output of the mouth, the output of the articulatory system, and the output of the phonetic computation (which takes phonological outputs as its input). The import of these distinctions is that the idea of acoustic differences "no matter how minor" is actually a misconception of acoustics. As you probably know, if a speech event is recorded by multiple microphones (e.g. a "stereo" microphone) which are the "same" from an engineering perspective, the resulting waveforms will be different. Acoustic waveforms will always differ by some small amount, and clearly we would not say that my choice of microphone brands or positioning brings about allophonic differences.
You have to start with some kind of definitional distinction, which I maintain is the "categorial" vs. "continuous" distinction -- phonology is categorial, phonetics is continuous. You also have to have a theory of what kind of information a process has access to, for example, can a phonetic rule access the underlying form of a word (the conventional answer is "no"); can a microphone access the surface mental representation of an utterance (patently not); can a phonetic rule access the output of the phonological computation (probably, and this is where the discussion gets complicated). Given that, plus a proper grasp of the statistical logic behind saying "is same" / "is different", then the question can be answered, and would tell you that not all systematic detectable variation that can be attributed to surface phonological context is the result of a phonological rule.
