It all depends on the stipulations put into place when the land is transferred to the NPS. For example, in 1980 a huge amount of land was added to Denali National Park through ANILCA, the majority of which was to be designated as a preserve.

For the preserve additions, the Park basically just adopted all state fish and game regulations and maintained traditional use activities and access points (landing strips, atv use, boats, etc.) and maintains concurrent jurisdiction with the state. I would imagine these lands would function very similarly, but again it depends on the process and terms of transferal.