They should. I haven't rented directly from Enterprise in a while. The last time I did I'm pretty sure I booked on a AAA discount rate and there was even a bonus. I checked it, and I got 250 base points, and there was some promotion where I got 500 bonus points.
12/03/2012 Enterprise Hide Details
Point type: Bonus
Point reason: SNAT61-
Other Earning 500
12/03/2012 Enterprise Hide Details
Point type: Base
Point reason: SNAT61-
Other Earning 250
I had a few business trips where the company paid for Hertz, but I didn't try to link it to AGR. It was a special corporate rate though. I did link my Southwest account to that travel and got a bunch of points.