Been a long time since I flew an Allison engine, but here goes.
Avgas should not pose any problem in a RR300/Allison 250. Engine temps would be hotter and you might not get full power before overtemp, but that should be it, at least in a short term situation. In most turboprops, it's more of a maintenance issue than an operational one.
As for "electronic fuel computers", I don't think the RR300 has one. Best I can tell, it's got a nice 1950's technology hydro-mechanical fuel controller.