I wouldn't want to power out of the mud, for at least two reasons - if you're in deep, how close are the intakes to the ground and are you going to ingest mud/stones? And if you're successful, your tyres will be shedding mud during the takeoff - where will it go and what damage will it do? Any mud left on the gear will freeze solid during the flight - what problems might it cause? Oh, and how will those very expensive brake packs fair with a dollop of mud inside them?
Powering out of the mud would be unwise and irresponsible IMHO.