Using an op amp as a buffer
If the datasheet says it is unity gain stable, then yes. Unity gain stable means precisely that the op-amp will be stable when used as you describe.

Do be sure the feedback path is short. If you make it long, then its inductance is increased, and maybe weird things will happen. No need to be extremely paranoid on this point; just don't go routing it 10 inches around the board and you should be fine.