My opinion. I would carry a spare tube, AND a repair kit. The first puncture gets the tube, and you can repair the punctured tube at home. If you're unlucky enough to get 2 punctures, then you'll be able to repair the second one on the road.
Now, as to repairing without removing tire and tube? It is my experience, that it can be difficult to find the cause of many punctures. I often have to examine the tire very carefully, to find the offending (usually) tiny piece of glass. If you don't find and remove it, you'll soon puncture the new tube...sometimes before you've finished inflating! Now, I guess if you happen to find a thorn, wire, or nail poking through the tire from the outside, then you know exactly what caused it, and can easily remove it. I'm rarely that lucky. Glück auf!