No, ATC are only recorded when making or receiving calls to/from aircraft, or when speaking to other controllers on a coord line. General conversations are not recorded.
This is not the case. If you do a search for CVRs on the internet you'll see that everything is recorded, not just transmissions between other aircraft. Two examples I can think of: the CRJ crash at Lexington in 2006 and the 737 overrun at Midway in 2005.
The lesson here is obvious!