On the older revision A501 (the one with the brownish PCB and 16 256Kbit X 1 DRAMS (120ns) there are only two layers in total (top & bottom).
I've recently modified my A501 to do the lithium coin battery mod. I had to remove much of the copper around the solder pads where the NiCad was soldered, otherwise I would've needed a 100W soldering gun with all that heat-wicking copper in place. Holding the board up to the light I can definitely say there are only 2 layers. IIRC mine is a Rev 5 A501.
