You cannot close the trap-door cover as the heatsink and fan will be in the way (sticking out), however the card can still be plugged into the CPU slot. What you could do is raise the entire A1200 desktop with two raisers (this can be anything from two books, wooden poles, or anything similar that's thick enough) in order to use the card with desktop A1200 units, without removing the necessary heatsink and fan (necessary as the 040 definitely should not be used without at least the heatsink).
EDIT: And of course you would need smaller simm modules in order to fit everything into the desktop case. The 128MB simms are too large.