Can I install a new fuel sender unit on a 72 duster without removing the tank?

You can, but why would you? If the sender is faulty, it could be rusted badly and the rest of the tank could be a mess and need cleaning out. Also would give you a grand opportunity to inspect the tank. I'd pull it. It's a 15 minute job.
ABSOLUTELY CORRECT. There is a right way and a wrong way to do this. Since the car is new to you, you have no way of knowing what shape the tank is in. RRR might be exaggerating a bit when he says it is a 15 minute job, maybe I'll drive to Georgia and time him on a gas tank removal, but it really doesn't take long. Then you can pull the sending unit and thoroughly inspect the inside of the tank. Clean it out, or get a new tank, if yours is really gross inside. If it is the original sending unit, have it rebuilt. Everyone on this forum seems to think that is best. Otherwise, I would get a new one. I know a lot of people have had trouble with the new ones, but I got mine from Classic Industries, and it works great. Then you will have the opportunity to install the new sending unit with the new seal and install a new filler neck seal. No more leaks AND you absolutely know about entire fuel tank.