When I arrived for a scheduled meeting, I was asked if I was Mr. Smith. I replied, "That would be I." It sorta sounds OK, if not awkward, just more formal. Would "that is me" or "that is I" both be acceptable?
Most people would say "That's me" or "That would be me".
"That's I" and "That would be I" are following a rule that somebody made up a couple of hundred years ago, and fooled everybody into thinking was English. So yes, they are grammatical according to the grammar that everybody was taught when people were taught grammar. But hardly anybody says them.