It’s an interesting question. I think the basic argument for “no” is that the penalty is removal, and he’s already gone, while the basic argument for “yes” is that the penalty also includes not being able to hold an office of trust in the future. (Related – Rubio says it’s arrogant for the Senate to tell voters who they can vote for in the future)
On that second point, how far does it go? Can Congress impeach and convict someone who’s been out of office for years? What if, for example, Obama wanted to run for the Senate again. Could a Republican Congress impeach and convict him, thus barring him from that office?
I lean toward the opinion that trying to parse the language is largely posturing and justification. The real question about impeachment is whether they can get away with it politically. I don’t believe the courts can review an impeachment, and I don’t see why they’re bound to follow precedent. The only review is the voter.
From that point of view, Congress can impeach and convict for any reason they think they can explain to the voters.
My prediction is that the Senate will not convict, but both sides will use it to grandstand. They’ll all enjoy the distraction and the attention. Anything, you know, to avoid that nasty business of passing laws. And it will be so very unifying.