If you are talking telephone quality (7kHz sampling rate, 8 bit resolution), I'd say recording audio with a 8051 is not impossible, although an 8051 would not be my immediate design choice, and I'd look for a specialized chip first. The problem, as you rightfully mentioned, is memory. You'll be eating through your memory at about 8kb/s. 64kb of memory will be filled in 8 seconds.
When a hard disk comes in to play, an 8051 would be out of the window as far as I was concerned. Now THAT's a tall order for an 8051, and definetely a wrong design choice.