No you don't necessarily need a server specifically. You just need a location that everyone has access to.
Access is a bandwidth hog, so you need a LAN connection, no wireless, no internet drives, local.
As for NAS drives, i avoid them. Typically, they don't work for multiuser Access databases, but not all NAS drives are created equal and some can support it.
Personally, if you don't have a server, then try the NAS but dont be surprised if it doesn't work. Then the solution would be to create a shared folder on someone's PC and share it from there. In that case, don't forget to stop frequent backups!