I can only speak about deciduous trees from my experience, but here's what I've found. All cuts about 1/4" and up should be sealed. Why? Mostly to prevent desiccation at the spot of the cut. Now, I'm coming at this from the tree collector's perspective, meaning I have to keep that collected trunk alive and intact. Chopping exposes a lot of xylem surface area. The xylem transports moisture from the root area to the above ground part of the tree. If you seal this upon collection, no drying out and you maintain moisture the length of the trunk. This supports back-budding. If you don't seal, the risk of dieback or outright loss is very high.
Now, the principle for branching retained upon collection is the same, only the risk is generally limited to the branch itself.
If you remove a branch altogether, I would advise always cutting outside the branch collar to promote rerouting sap flow. You can come back later and carve the area. If you cut too deeply at first, you risk dieback down the trunk from below the removed branch to the roots on that side.
As for promoting healing, I have no idea if cut paste or sealant works. I do know that collected deciduous trees recover better when it's used, solely due to moisture retention.
FWIW.