It may depend on the Mono model. I've carried my Les Paul and other guitars with tilt-back headstocks in M80s for over a decade with no issues. I don't throw them off of trucks though. I'd be less inclined to use a Vertigo, Sleeve, etc. for such an instrument.
Note that if the Thundergun has a scarf joint at the headstock, it probably won't ever break there.
Bass content: I carry my Gretsch G2220 (w/tilt-back headstock) in an older-style M80 that I originally bought for a Les Paul. My Decision P has an M80.