I've been using road bikes for 33 years touring and have used both panniers and trailers. I've always used 700x23 (or equivalent) and have never had a problem. I have toured only on paved roads, however. I always carry several extra tubes and an extra tire.
There are "road bikes" and there are "road bikes".
I had an '83 Trek 400 and now have a Surly Pacer as my rain/errand bikes. Both are certainly "road bikes", not dedicated touring bikes, but have drop out eyelets to accept a rack, long enough chainstays to avoid heel interference with reasonable size panniers and I have them geared suitably. I would not hesitate to use either for touring and many other older road bikes share their capabilities.
Then there are "road bikes" that are dedicated sports/racing designs with short chain stays, tight tire clearance, no eyelets and tall gearing and these are far less suited to use for anything but the lightest touring in reasonably flat areas.