Maybe not. If the car you have is corporate car and attempt this at a franchise location they may not allow it.

I had this to happen on a OW from DEN (corporate) to SLC (franchise). Since my return was a corporate return, they had it reserved for another OW back to a corporate location. I had to swap to a local car since it would be returned back to SLC.

So, YMMV.

As for parking, SDF did not have on site parking when I had a sort of local rental, I had to park in economy at the airport.