I guess if someone went through the effort to prompt an LLM for a thank-you card note, and then transcribed that by hand to a card and mailed it, that would count. It's somehow more about knowing that they are making some actual effort to send a personalized thank you than it is about who wrote it.

But honestly I don't think "blank page syndrome" is very common for a thank-you card. We're talking about a few sentences expressing appreciation. You don't really have to over-think it. People who don't send thank-yous are mostly just being lazy.

My financial advisor sends out Christmas cards and Birthday cards. They are pre-printed stock cards. I don't even open them. I should tell him not to waste the money. If he even wrote just one sentence that expressed some personal interest, then they would mean something.

These kinds of messages are on the one hand just pro-forma courtesies, but on the other hand they require that that some personal effort is invested, or else they are meaningless.