Are you asking OOG or IG?
OOG: Yeah I don't see why not, so long as you follow all the rules. I don't have a rulebook on me but I think you need a rank of alchemy (or maybe 3?) to mix elixirs into stuff, so good luck even finding a server with that skill.
IG: Well, I don't know, can you? Ask the tavern workers. I'm pretty sure it's illegal even if the tavern does it.