It's definitely not recommended. Growlers aren't really built for the pressure of carbonating. At 70 Degrees F, carbonating a beer to 2.5 Volumes (pretty standard) would generate roughly 30PSI. The large surface and thin walls of MOST growlers aren't made for that.
If you had CO2 and a regulator, they make carbonating caps, these could be used to force carbonate at lower temps, to carbonate to the same volume at 34F would only be 9-10PSI.
TL;DR If its a super sturdy growler, give it a try in a place it can explode without ruining anything! if not, don't.