He was exhausted enough that he took the quarter staff to use as a crutch since he had trouble walking on his own. And while real world experience is definitely good, being trained to use a sword isn't meaningless. Especailly when the experience that Mat had up until then was mostly lying on his back because his dumb ass was sick from the dagger. Besides that, I don't really remember Mat fighting much of anyone in the first two books. He was always just trying to survive the onslaught, if he wasn't lying in bed sick. The whole gang in general have done very little fighting. They mostly just tried to escape. Besides THAT, even if he did fight, I'm fairly sure he said this was the first time he wielded a quarterstaff, so any real life experience transfer would be rough at best.
So heeeeeeeeeeeeeeeeell no, it wasn't earned at all. Imo.
Straight out of that scene:
"I think ill put my trust in a good bow, or a good quarterstaff. I know how to use those."