This is a surprisingly popular one, and actually has historical prescedent - it was first claimed as far back as 1628!.
Apart from the fact that at the time the crew were in battle, so sightseeing was probably not a priority, Southsea Castle is over a mile from where the Mary Rose sank. Even at his widest girth, Henry would have been nothing more than a small dot on the coastline.
Out on the wreck site there is a marker buoy, about 3 metres tall. If you look out from Southsea Castle, where Henry VIII watched the ship sink, it’s a speck on the water. You can see it clearer with a telescope, but they weren't officially invented until 1608. Therefore, there was no way they would have seen him, identified him and thought it was worth looking at.
On a related note…
1a. “The crew all rushed to one side to see a whale/dolphin”
1b. “The crew all rushed to one side to see a mermaid/sea monster”