I think the problem is that “at your earliest convenience” is a formulaic convention that uses explicit, almost exaggerated politeness to basically issue a stern direction, meaning “as soon as you possibly can”. When you turn it into “at my earliest convenience” it’s unclear if you mean “whenever it’s convenient for me to get to it” (what the words say) or “as soon as I possibly can” (what the meaning of the formulaic original is). Or else it sounds like you didn’t quite understand how “at your earliest convenience” works.
Personally, I’d think it’s funny to receive an OOO like was in the video, at least the first time. It wouldn’t fly AT ALL at my company, but it’s at least interesting. All I really want to see is how long you’re out, and who I need to contact instead.

I worked for a federal contractor back during the Great Recession when government offices were shut down/working with a skeleton crew. I still remember getting OOOs from almost every email address in the agency we worked at explaining they were on furlough & to contact one specific person if the issue was urgent. We all assumed this poor person was hiding under her desk, rocking back & forth, with her head in her hands.
As for this one I think it’s fine for internal particularly if someone can “read it in her voice” and knows she’s quirky but I’d probably just do a short one for external (or none? because I’ve heard there is some kind of security risk with them?)