no, you need a waterproof cover. Fabrics have come a long way since you were in nappies
You aren't going to want to wash bedding everytime baby goes to sleep. The PUL fabric in most mcn is waterproof and breathable.
If you don't want to use pul, then think about using wool. A lot of people knit shorties to wear over nappies, it wouldn't be rigid enough to keep a prefold in place though.
I wouldn't choose a osfa cover - you really want it to fit snug over the inserts and round the waist and legs to stop leaks and to stop the insert moving around. A osfa cover is not going to work with a newborn.
The wraps are really cheap, and you can pick them up for $5 or $10 on TM, worth the investment to get ones that are likely to fit