Short answer: No.
You cannot use an existing Fallout: New Vegas save to play TTW. Even though a save might load, there are too many changes for it to work correctly. No support is provided if you do this anyway.
Saves made with previous versions of TTW will not work with 3.x. Too many changes were made to allow saves to be compatible.
But it's also an 18 year old movie, so it doesn't do much to disprove that good comedies don't get made any more.