In most cases, you want to let the tile sit overnight before walking on the tile. After the floor is grouted, you should wait a few hours, then put down some cardboard and have the toilet installed. Keep the cardboard down for the rest of the day to be sure nothing falls into the grout lines while it is still setting.
Another alternative that would cost you extra money, would be to have the tile setter lay the area by the toilet (and pathway to get to it) in a quick set thinset mortar...stuff dries in a couple hours and the tiles can be quickly grouted and the toilet set back in place. The rest of the tile could then be set in normal thinset or the entire job could be finished in the quickset mortar.
Quickset mortar is expensive and much harder to work with, but it may be an option here if your tile guys are familiar with the product!
Otherwise, plan a visit to a friend's house or look into a day at a local hotel with daily rates...might be nice to simply get away for a day or two while they take care of this!