Does Mary Sue use a sword or other bladed weapon in a high-tech setting? 

Yes, any chracther who use a sword in high tech settings are Mary Sues.

The best way to get around this is using a something also high teck, like the Chainsword from Warhammer 40k.

Though why bother at all when a flame thrower or laser cutting device works just as good.

Yes, my character uses a high-tech sword based on the energy sword from halo, just less high class, and it's made in a blade-like fashion to cut through the high-tech armor that the other side has.