Why not?
Edit: A little searching here seems to say that synthetic ethanol can be used as a food ingredient and must be accurately labeled. The policy doesn't say that it can't be used in beverages. However, I assume that it's use in many beverages are defacto banned as synthetic alcohol is not part of the tradition grain bill. I don't see why it can't be used in the liquors or a new type of beverage.
https://www.fda.gov/regulatory-information/search-fda-guidan...
Another edit: it appears that FDA lists ethanol as GRAS for general food product use, and that TTB approves the use of GRAS ingredients. If you use synthetic flavors, it looks like that affects the labeling. I assume you would just have to label the alcohol consistent with it's source.