Yes, presumably. The most obvious hypothesis is that it was the version of standard Indic prevalent around Avanti around the time of Ashoka; and while it’s not really certain, I think the obvious thesis is probably the correct one in this case.
They were mostly Sanskrit, but there would have been a variety of dialects. The later Mahayana and Abhidhamma texts would have been mostly or entirely in Sanskrit. The early texts of the (Mula-)Sarvastivadins would also have been in Sanskrit. Some, such as the Mahasanghika Vinaya, were presumably in Hybrid Sanskrit, the standard language of that school. The Gandhari texts that have been identified from manuscripts belong to the Dharmaguptaka school, so it’s plausible that the Dharmagupataka texts in Chinese were from that language; that includes their Vinaya, and maybe DA.
We don’t know, however, that each school consistently used one language. And it is difficult and uncertain to infer back from ancient Chinese to specific Indic forms. We have to look at a specific Chinese character—typically used in a name—and infer back from the pronunciation of that to a specific Indic dialect. But knowledge of ancient Chinese pronunciation is often derived from Indic translations, so it gets circular very quickly. And there are all kinds of complications, like regional variations in Chinese pronunciation, and so on.
It’s possible that some of the Chinese texts were translated from otherwise lost dialects. However, so far as I know, there isn’t any compelling evidence that this is the case. Bear in mind that most of these languages are very similar anyway; so far as I know, the Chinese texts themselves just refer to the Indic languages under one generic name, usually translated as “Sanskrit”, but perhaps meaning simply “Indic”.
Note that I said earlier that the Chinese texts weren’t translated from Pali. This is certainly the case for the nikayas, but it is a little more complicated than that. Several texts were brought from Sri Lanka to China for translation, including a Samyukta Āgama. However, these were, for the most part, not Pali or Theravadin texts at all, but manuscripts from other schools that just happened to be sourced in Sri Lanka, at the Abhayagiri Vihara. However there are perhaps a few later texts that were in Pali: the Vimuttimagga, and the Sudassanavinayavibhasa, the Sinhalese Vinaya commentary. We can’t be sure, but Pali is a possible candidate for the originals of these (although they may have been in Sinhala Prakrit. Did I say it’s complicated?)