“Should dentures fit without adhesive?”

Yes

Sometimes you may need some adhesive to make them more stable. Dentures fit better if there is more available bone support in the mouth.

It depends. Sometimes even the best made denture may need a little help with retention from an adhesive. Other important variables to consider are the size of the remaining ridge and the type of saliva. The bigger the ridge, the more likely the denture will not need adhesive. The lower dentures often have small ridges and will often need adhesive even for the best made denture. The saliva may also affect the retention. If you want more security, use an adhesive.