We do have a reasonable Nahuatl corpus, and it remains a (very minor) spoken language, so if it is such, there's a good chance it could be understood. But there's plenty of extinct indigenous languages with very little or no attestation, and if it's one of those, well, hopefully it's related to something we still know.
The orthography remains a problem, but it's quite plausible that some friar somewhere in Mexico came up with this European-derived script to transcribe the local language, and it didn't stick for any number of reasons. There are several non-standardized Latinesque orthographies we know (see Carochi) for Nahuatl, so it's a known phenomenon. (And there's still no standard system!) The hand of the Voynich seems reasonably practiced, so it must've had some use, but it could possibly still have been only one man over a few years. (It's clearly not an indigenous script.)
The friar involved could perhaps be called too clever for his own good; imagine if St Cyril wrote a few books in his script and then died of bad gruel, and some Pope got hold of them. Same sort of thing. If the (theoretical Spanish friar) Voynich author had been less inventive, we'd (if this theory is true) have long since understood it.
Anyway, hopefully a few Meso-American language experts can take a look and decide if there's a possible match.