How to install floor baseboard on drywall frame with metal studs?
If the walls and baseboard is all perfectly straight, it would likely work -- but everything won't be perfectly straight.

I've used liquid nails to attach baseboard before (in a similar situation), and it does work except where there are bows in the wall or baseboard. 

I used finishing (or brad -- I don't remember) nails to both hold it while the glue sets and provide some re-enforcement where needed. Install two nails nearby at opposite angles -- essentially forming an "X" if you were looking straight-down on them. This is a lot stronger than nails going straight in and will resist pulling out.



You can caulk the edge between the baseboard and wall. It makes it look significantly nicer, IMHO. I use bright white for that. Normally the edge touching the floor isn't caulked but if it makes sense in your situation you can do that.