Is it ok to calk drywall corner joints rather than taping them?
I have been seeing this a lot lately so I don't know if there is a new caulk on the market for drywall but in my experience the caulk will 'flash' under paint so it isn't going to give you a good finish and it will be noticeable. I would ask the worker what type of caulk it is and how it handles being painted.