For the road caliper, a deflated tire of any width will pass between the pads. If you're in a repairing-flat-tire situation the tire is likely to be deflated when you remove the wheel, so no problem, and you can defer inflation of the repaired tire until after you've re-installed the wheel. Not ideal, but not a big problem either, assuming time is not of the essence.
As a practical matter, a given bike frame will either accept road calipers or cantilevers - so you won't actually have a choice.