No, Maintenance Mode only applies to the electronic parking brake in the rear. So if you're doing rear brake work, like changing pads and/or rotors, or servicing calipers, the car should be put into Maintenance Mode. For everything else, it isn't necessary.
If they end up replacing the tire, you may want to make sure they use a new valve stem kit instead of reusing the old one. It's just easier to do it with the tire already off and I believe the kits are fairly cheap. You may also want to have the wheel with the new tire rebalanced.