My first thought is "NO!" It is quite likely transmission damage will result due to lack of lubrication of the output shaft bearings and seals.
However, it is possible that a driveshaft disconnect can be installed, which would allow towing.
OR, you could just get underneath and remove the driveshaft from the differential yoke, wrap tape around the u-joint caps to hold them in place, and tie the driveshaft to the underbody securely. Be sure to put the u-joint fasteners in a safe place so the driveshaft can be reinstalled.
The Owners Manual, if you have it or can get it, might have towing instructions.
Keep in mind that Buicks are not exactly lightweight vehicles. It wouold be a good idea to weigh the car. It is likely that a Class C is limited to 3500 lbs or less towed load.
Good luck.
CM1, USN (RET)
2017 Jayco TT
Daily Driver: '14 Subaru Outback
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