I have folded a pf in thirds and just laid it in there, in fact some wahm's make prefold style stuffers just for that. I've done this with my old Tuesday Bear side-velcro-ing wool covers and it always worked fine. And I've done it with the basic fold when I couldn't find my snappi, and just kept my fingers crossed....
I would be careful about changing tho..... if it's a toddler on the move who can undo his own cover, then that could get messy
I do sometimes, and it works okay, but i don't think it's the ideal way. The prefold can slip around a lot, and you get poop on the covers, and it also tends to be bulky. I only do it because my DD's in the squirmy crawling away stage, and it is sometimes just easier to only have to put one thing on instead of two. But I highly recommend pinning or snappi-ing if you're going to use prefolds on a regular basis.
I know quite a few people who use a diaper service, and virtually all of them do the trifolded prefold in a wrap thing. You just have to have more covers. I trifolded when my son was too big to snappi his premium prefolds around his waist. Now we have sized up to toddler prefolds and we can snappi again.
Besides trifolding, I have also used a prefold w/o a snappi when I had the diaper all folded around the baby in a fold where you would normally pin or snappi (sidewall/jellyroll, angel, newspaper, etc.), when dang it where did that snappi go! In that situation I just hold the prefold shut around the baby with one hand and close it up with the other, and have had good success with it all staying together.
I agree with pp that you want something nice and snug, so velcro is better than snaps. I have one snapping cover made out of fleece that works because I stretch it and snap it nice and tight. But if the cover is made of a non-stretchy fabric, I don't think snaps would work.
I think it's worth it to learn to snappi though, because then you can let the babe go coverless around the house sometimes, which is nice for their skin. Also it's easier to tell when they have wet.