The 1976 Royal Flush uses a deeper cabinet that Gottlieb had adopted earlier that year. The Abra Ca Dabra cabinet is the shallower cabinet where the coin slots are above the door instead of on the door. Without going out and measuring, I can only speculate that the bigger cabinet has the same width. I think it would work, but you might wish that certain cables were longer, and you may have to change out some hardware at the bottom of the playfield to engage the different lockdown mechanism. Be sure to check the positions of the four backbox bolts, too.
If you do this, it would be a service to The Pinball Community if you wrote up some notes on the adaptations you had to make.
.................David Marston