Thanks Estelore.
Of course, we have no way of knowing exactly how the translator chips worked, but it would make sense for the chip to still work even when in morph (since the chip was connected to the mind and the mind is still connected to the person even in morph). It's logical to assume that the translator chip not only translated foreign languages, but may also have allowed the Andalites to "learn" the language.
In book 14, Ax is able to translate the
Galard used by the Horse Controllers. This proves that either Ax's mind is still connected to his translator chip when in morph, or that he already knew the language before hand (either by naturally learning it or via the chip itself).
However, there are some inconsistencies in the series regarding languages. In book 13, Ax admits to knowing some of the Hork-Bajir language, but is unfamiliar with certain key words that Jara and Ket keep repeating. This could imply that Ax does not have a translator chip (I don't think it's ever said for sure that he has one) but that would be strange since it was said in Andalite Chronicles that all members of the Andalite military had a chip implanted (Elfangor had one even at the start of the AC).
Interestingly, we know for a fact that Aldrea did have a translator chip, despite the fact that it was clearly stated that she was never in the Andalite military as females were not allowed in the military at the time.