Originally Posted by Happy Feet

Sorry but no.

First or easiest is to remove the area of tube on one side, patch and repair while wheel remains on bike IF you know where the puncture is and the cause is easily removed. This is sometimes called the Dutch method.

However, if the cause is unknown, as is often the case, it's a royal pita to try to rotate and work on a tube while the whole thing is pulled out of the tire (in order to find the source of the flat). At that point it is easier to remove the wheel so you can feel inside the tire for the offending sharp object while making note of where the tube and tire line up. Avid cyclists often carry a spare tube and just swap that out so they can patch the punctured tube later at their leisure, not on the side of the road. But if you don't find the source of the initial puncture you may just wind up with a secondary flat in short order.

To remove the wheel the easiest method is to have a quick release skewer, not a removable triangle or spreaders for the stays - I've actually never heard of that before. With Al or CF you will probably crack the stays and with steel that procedure is called cold setting, usually done for about 5mm or so to fit a modern hub into an old school frame.