I've always taken them apart when that's possible. When it's not, I've sometimes wrapped a wet rag around the center of the fitting before soldering. I have no way of determining whether it helps, but if the rag is still steaming (not completely dried out) when I get a good soldered joint I figure it's probably provided some cooling at that location.
The problem with damaged valves is that they usually work fine in the open position. A valve that is permanently open during normal use---the shut off for the supply side on a water heater, for instance---may not let you know that it's not going to work just when you really need it.