Dialects degenerate phonemes that would otherwise occupy identity relations between different utterances of the same "word" (word/concept mutable hyperobject as is the standard in any socially-relevant spoken language) which would be a bit of irony in this thought experiment since common knowledge dictates that more data samples must be present in the dataset (not less, as in rarely-spoken languages) to associate separate pronunciations of utterances representing the same underlying concept. However very-rarely-spoken languages probably don't have distinct dialects since so much focus is put on mutual intelligibility with the few members of the group that remain fluent in that language. It's not outside the realm of possibility that small speaking communities nonetheless fractionate into dialectical specialities but that seems increasingly unlikely as the fervor for preserving/recognizing dying languages increases, and global instant communication continues to become more commonplace.

Example: Schwabisch is wild and would be phonetically transcribed very differently from Hochdeutsch which is its ostensible language progenitor (technically more a cousin than an ancestor in the lineage of language evolution), but if the goal is merely to focus the model purely on phonetic transcription then you can add additional post-processing layers which map sounds to core concepts shared across dialects for actual translation. But I like your idea of interacting with the intermediate elements to familiarize yourself at least with the phonetic patterns, we humans are still thinkers enough to infer patterns of grammar and semantics from these building blocks just as we have done for the entire history of the species/lineage before written representations of language came along (relatively late -- evidence of script cropped up only once civilization had centralized to a sufficient degree to make economics non-local and non-trivial).

tl;dr the big words: it's not til you collect enough spoken samples of the dead(ish/dying) language being spoken that the local idiosyncracies are discovered, luckily linguists are smart enough to probably anticipate and certainly post-process language snippets to grasp the common structures for this or that given language.