Possibly. It depends on what is wrong with it and how the AWD is setup in the vehicle. About the only way this could work is if a rear drive line had gone out (like u-joints) and it was removed. The rear differential would free spin and the front wheels would provide the drive power. Overall, as compared to the rest of the system, the driveline is a relatively cheap fix, so I doubt this is what you're talking about.
That said, if almost any other part of the AWD system which transmits power to the wheels goes out, you're going to be out of luck. Take for instance the differential. If the rear diff goes out, you aren't going anywhere. If the transfer case goes out, there's no transmitting any power anywhere. If the system is engineered to provide power to the rear first, with the front used as backup traction, that's not going to work, either.
Really, if the AWD system is broke in an "expensive way", you are pretty much either going to have to get it fixed or let the vehicle sit.