Mechanically yes. Doing so and maintaining the feel of D&D not so much. Calling magic something else and just labeling it as a power source is basically a transformation to the supers genre. Everyone just has these cool powers that work somehow and they form a team of crimefighters...err.. adventurers.
But maintaining the feel of D&D should not be so hard.
And it isn't.
Had Cantrips been 1st level spells that you cast and let you do something at will for an hour or two, few would have complained if you gave the caster a bonus spell slot to jam it in.
Same with mundane class.
If you take a bit of the fighter's power or rogue's skill, boost it a bit and tie it to a believable resource (rage, kill, focus, fatigue, etc), I doubt many would complain.
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What about a roguish class that has Ideas. It thinks up ideas on how to trick the enemy or new approachee to skills. But of course, eventually the genius "runs out of Ideas".
"How about we... ummm.... I got nothing. Sorry. We're screwed."