Wiring question converting 120to 240
Yeah, sounds legit.  Generally since the circuit served the A/C before, it is typical for those to be dedicated circuits and thus homeruns.  If there are onward wires, you'll know when you open up the socket.  

You can fit a 15A breaker and NEMA 6-15 recep(s).  Feel free to use a dual 6-15 so you can just keep the same faceplate. 

Or, you can fit a 20A breaker, and fit either a) any number of NEMA 6-20 sockets, or b) two or more NEMA 6-15 sockets. 

Oh, one more thing.  Code requires that a receptacle exist within 6' of any point along walls (following the walls around corners, not straightlining).  You must make sure eliminating this 120V socket doesn't make you fall short of minimums.  If it doesn't, that's good evidence that the socket was installed specifically for the A/C, and may have even been 240V once upon a time.