Absolutely, if writing in them counts as acknowledgement.
While the vast majority of written works were in standard (Classical) Latin, there were some things written in the non-standard dialects. Gaius Petronius' Satyricon has sections showing the Latin of the general public of Rome, which differed from the standard acrolect used for most writing. See this section of the Wikipedia article for more info.
Another good example is Peregrinatio Aetheriae which was an account of the authors trip to the Holy Land, also written in a non-standard Latin dialect. This was written around 385CE so it's right in your timeframe.
There are more sources, but this should give you an idea.
As a general rule, in most cases where there's a large empire and a standard language, it's inevitable that someone somewhere is going to use non standard dialects, even if only for effect in an otherwise standard piece (such as the dialect of a character meant to provide comic relief).
hi! not discouraging other responses, but you may be interested in a few previous threads