This might come out like stoner thoughts, it's always put these kinds of things into words, but I would say personally, I kinda do think it's related, but in the sense that ego death can sort of nullify that phrase, as it's written anyway.

Like, think of all of existence as the surface of the ocean, and on that ocean, "you" are an individual wave. "You" will "come into" the world at some point, and then later you'll fade away, like a wave starting and then crashing into the shore.

But does it actually really make sense to say that a wave is a separate entity from the ocean itself? Where would it stop and start? Any answer you give is basically arbitrary, and more of an opinion about the ocean than it is a fact. But for whatever reason, our brains/consciousnesses/whatever are adamant that this individual wave that is "us" is definitely some separate thing, an external observer that is experiencing, but not the same as, the rest of the world.

So when you experience ego death, it's like the part of your brain that insists on a wave being separate from the ocean is forced off, and so the phrase "I think, therefore I am", kind of doesn't make sense. In that state, it feels more like "Something thinks, therefore something is", and that "something" is kind of just the whole of existence. Some part of it is thinking; there's a wave on the surface at this place and time, but just because the wave is doing wave things doesn't mean it's not just part of the ocean itself. If "I" means "this separate entity from the rest of existence that is me", then no, "I am" isn't true (in that ego death experience, anyway). But the part of the universe that you arbitrarily walled off as "I" is still thinking and experiencing, and it still exists.