No problem doing what you suggest, and with an axle that has decent bite on the face it'll stay put very nicely. OTOH, of you have a more modern hub with a plain (non-serrated) axle face, especially an aluminum one, the hold won't be as secure and a hard bump may shift the wheel.

Also life is easier if you can simply slap a wheel home and know it's in the right place. If you're not comfortable filing, consider using a bit of body filler in the opposite dropout to limit how far the axle goes.

Afterthought --- I let this go earlier, but in retrospect, I can't understand why the dealer couldn't do a complete job using the 478 tool. The normal correction is to curve a blade slightly to get the two dropouts to the same height. It's a very easy job using the gauge.

So either you have a mechanic who doesn't know how to use the fork gauge and do the job right, or possibly the fork is OK, but the wheel is off. Eliminate the second possibility by flipping the wheel and seeing if it's still off to the same side. If so, go back to the shop, and have someone else finish the job properly.