No, not really. The game-code is the "mod" part (i.e. jampgame, cgame, ui) and the engine is jamp/jampDed.
You can run the OpenJK engine with JA+ gamecode with no issues.
You can run any engine with the JA+ gamecode and a vmMain/syscall proxy-mod intercepting some code between engine<->gamecode. It doesn't run in parallel, and you can't combine e.g. JA+ and clanmod. The proxy mod is a heavily stripped down piece of code to intercept e.g. a few commands. It can not interact with the existing gamecode, it's very limited in what it can do.