Unlikely. I remember doing this sort of thing back in the early 90's with drives, but nowadays the drives are factory calibrated once the PCB's are installed, so it's pretty doubtful. Of course you could always try if you happened to have an identical dead drive where it had failed mechanically and therefor you knew the circuit board was good. I doubt this is the case, and you wouldn't rip a PCB off a working drive to test the theory.
Also, removing the PCB would be tricky, sometimes manufacturers use security screws or other tricks to make removal or disassembly of the drive all but impossible.
Drives are dirt cheap of course, but this doesn't solve data loss problems. Forensic data recovery is impractical due to its cost. There might be some other things you could try if the drive was spinning up or at least making some sort of ticking noise or some sign of life, but doesn't sound like it. Sorry mate.
Problem solved! I followed the steps in this video (http://www.youtube.com/watch?v=29FztWJVxbM) and recovered every single file that was on the HD!! It was not that difficult and the parts cost me less than $10.