The measurments are the biggest thing. It may be short in the length. It all depends if your rear couch has a box built on one side. Some Deluxes and Airflytes had about a 4" or 6" wide box on the street side. My Deluxe doesn't have one and we have the original mattress.
I think the only other issue would be how the back portion follows the curve of back wall.
Well, I can't speak into whether or not it would work, but that is a cool idea if the measurements work!! I would definitely invest in a waterproof bed-bug mattress cover, regardless - you can get 'em at Bed-Bath& Beyond, Overstock, etc.
My Compact's got a permanent bed (PO's PO did that), but if this idea does work for you, you might then consider doing what I'm doing with my mattress. I've hired a lady to make this sort of giant pillow case thingy to cover my mattress when it's not in use - that way, it's more fitted for seating. We're using something like a thin quilt or coverlet (still landing on that) to do this, and I guess if I'm really tired after a day of camping, I wouldn't necessarily have to remove it, since sheets will be put on it either way.
Unless you think you might just go ahead and upholster the IKEA mattress, this kind of thing might work for your purposes, too?