I think in some ways it could be a really sweet thing to do.
In terms of the food selection for them, I don't see how it is that much different than if you had invited them to a banquet or had them at a dinner party at your home. In those cases, guests have most if not all of the dishes pre-selected for them.
If you think they would enjoy it that way, then it is fine. I do know some people love to scan the menu and see what appeals to them, so in that case it might not be the best choice.
Or are you wanting to pre-order because you think they would be hesitant to have as many courses, drinks, etc as you know they would enjoy so as not to run up your bill? My mom would be like that.
I would think this is surely not the first time CG has dealt with this, so they might have some suggestions.
In terms of leaving a CC or room key for payment - maybe a less risky way to go would be to load up a disney gift card with a bit more than you think the meal will be and leave that with the manager earlier in the day.
That way, there is room for little substitutions if they see something else they would like. You can then just go back the next day to collect the remaining balance on the gc and get a copy of the receipt. That way, your parents never have to see a bill at all.