I'd say you're spot on. I just did that with my neighbour's basketball net, to make it a little more permanent (got rid of the plastic base, set some abs pipe in concrete in the ground, and mounted it like that. Cut them at ground level, find some tubing that fits neatly inside, and use a bolt or get them welded into the upper post.

That'll be kind of handy.

Since we cannot see your exact installation, and do not know what equipment you may have, exact advice is difficult to supply. Be advised that the posts are that same outside dimensions as standard water pipes. Corner posts typically the same as 2" IPS and line posts either 1 1/4" IPS (often) or 1 1/2" IPS. Your posts may be thin gauge tubing from rolled strips of 16 gauge. Thin posts cannot be threaded.
Patching the posts will be a weak repair.

At the link, go down the list on the right side and click the links for threadless compression couplings and for setscrew couplings.

Another choice is the coupling for plumbing that is often called a Dresser coupling.
Given the equipment I have available, I would remove the existing posts completely and replace them completely and properly. Your situation may be different.

Here is a link that might be useful: Couplings

If OP can find tubing that's a tight internal fit and it goes a reasonable way into the ground, and a reasonable way into the fence post, like a coupling, it won't be a weak point, it'll be the strongest part of the post.

Thanks, all good suggestions.

"If OP can find tubing that's a tight internal fit and it goes a reasonable way into the ground"

The inside is often filled with at least some concrete if the pipes are set in concrete.

Thanks for that warning. I will see if they can can be cut somewhat higher than ground level so a patch can be applied. If the wheel spacing on the truck is right, it should be possible.