It depends very much on the skills of the operator. An unskilled tech is likely to cause more damage, so that's the basis for my recommendation.

Btw, carbon is not the usual problem. It's a simple cleaving along grain boundaries in the solder, plus a bit of oxidation at the interfaces. Resoldering fixes that very well, thanks to the miraculous action of flux.

Skip the sucking step unless a) you are skilled and B) the joint looks like it's crud-filled.