Yes. If you want to give it a try, there is some good info in the video below. That guy has built roadworthy DIY electric cars in the past but he gave up trying to make this concept work. There are a few points on which I think he could have improved his chances of success but didn't. You might succeed where he failed.this would need a variable frequency control box if run from battery/inverter ?
He is using an automotive alternator but the concept is the same. One difference is that an automotive alternator which is three phase, and yours is (I assume) only single phase. Three phase is much better for motor control applications and there are plenty of controllers out there for 3 phase (not three phase with rotor excitation regulator tho). There is almost nothing for single phase.
One thing I think he needed to try but didn't, is adjusting the rotor current in response to load. He just fed it a straight 12V and think that was part of the problem.