I think it does.

I have, in the past, seen [dead] comments that (IMO) shouldn't have been, clicked on "vouch", and when the page refreshes they are no longer [dead].

Or maybe HN just shows it that way to me and it is, in fact, still [dead] (kinda like hellbans).

It actually brings them back, they do not lie to you about them not being [dead] anymore. I've vouched for a number of shadowbanned users when they have a comment that ought to be visible and then other people reply to it. You can verify (should you run across this again) by logging out or using incognito mode to view the page after you vouch.

I've noticed that sometimes [dead] comments don't seem to be revived by - presumably - just me clicking vouch. Perhaps vouches and flags and other criteria are balanced against each other or something like that.

The OP article explains that vouch only works once, and if there are more flags it stays dead.

I'm pretty sure it works in the obvious way.

I would guess that some comments take less vouching to be reborn than others though.

It definitely does work. I suspect that vouching (like voting itself) has an influence weighted by the reputation of the user in question. Reputation being some secret sauce correlated with, but not identical to karma.

The value of vouching, like everything else on HN, is secretly manipulated behind the scenes depending on how much you agree with the hivemind. If you vouch for things that then get flagged again (because the hivemind doesn't want to read them,) your vouches will carry less and less weight.