In short, no.
For example, the fastest official CPU board that the A1200 can take is a 603e @ 240MHz (overclocked versions also exist), on a 32-bit wide memory bus. The fastest A4000 board uses a 604e @ 233MHz on a 64-bit wide memory bus.
The A4000 has a 32-bit wide Zorro 3 expansion bus that is capable of supporting DMA. Almost everything you can put in an expanded A1200 will end up being PIO driven. As a consequence, PCI expansion buses tend to be more efficient in the A4000 than the A1200 (only obvious exception being the GRexx, which uses the local mini PCI of the cyberstormppc/blizzardppc in either case).
Whatever expansions there are for the A1200 that hang of various low bandwidth ports (eg clockport soundcards, USB etc) there are faster equivalents available for the A4000.