Well, well! How the times have played a hand in viewing this question.
I have not received a thank you note for the gift. I don't care, although I'm not especially impressed -- I still think the right thing to do is to write promptly upon notice, even if you have asked the company not to deliver yet.
(As an aside, it occurs to me: I have no idea whether they had it delivered already or have asked the company to wait. So if you are counting on your guests to understand that you are waiting to receive the actual gift, don't bet on it, because they don't know that you haven't.)
Anyway, I am not mad at my cousin (I forgot all about it, in fact). The reason I am writing is, as you have probably guessed, that there is a very good chance that this wedding is not going to happen in June because of the pandemic. I haven't heard anything about canceling or postponing, probably because they are going to wait a little while yet to see if it will be possible to have it as planned in June. That's what I would do; for our part, we haven't cancelled our hotel reservations yet, because although the odds aren't good, there's still a chance, so no need to decide yet.
But let's say that they decide either to postpone the wedding they'd planned, or just cancel it and get married privately with just an officiant standing 6 feet away (there was such a wedding reported in the NYT this morning) or something. I still want them to have the gift, of course, even if the plans change to something that doesn't include us -- it's for the marriage, not for the wedding.
Now what do they do about writing thank you notes? I can only imagine how stressful it would be to write them now; they are surely going nuts trying to figure out what to do about the wedding, and they couldn't really write about the gift without saying SOMETHING about the wedding plans now to people who all are waiting to know, but what could they say? But if they put the wedding off for an indeterminate time, maybe in the fall or next year, that's getting awfully long to wait to write. Now I'm glad that I sent my gift early and Zola notified them that I did! My part in this is over.
It would surely seem awkward to wait until after the wedding to thank people if the plans change so that those people are no longer invited. It's okay to make those plans, it just would make writing those notes tricky.
So to me, this situation underscores that the date of the wedding itself is completely irrelevant to when the note should be written. If the gift comes shortly before the wedding, no big deal if you wait until after (although I still wouldn't -- it's still nice to be prompt, and anyway, you'll be glad later that you wrote as many as you could before it became a mountain). But if the gift -- or the notification -- comes many weeks or even months before, write promptly.
I am sure that my poor cousin must be wishing that they'd already written their notes and not have it hanging over her like this.
She must even be wondering if they need to send the gifts back, or at least offer to, if they cancel the wedding. I know I wouldn't want them to, and I imagine that will be true of all the guests, but it probably would be gracious to offer. What would you do?