Yup, that strap holds the mast if that little metal arm comes lose from the screw. I actually had this happen in high winds with two people on the Bravo. The boat can flex a little bit, and that metal door can open. I made a couple minor modifications to allow the screw to sit a little bit deeper into the small metal arm, and Hobie has redesigned that metal arm since my boat has been made to include a hinge which allows the screw to sit a little bit deeper into that arm.
I can't see the little arm failing anymore on my boat, but it can't hurt to have that strap done up (and replaced) because if you do have a failure, that mast will come down in a hurry, and the way the tripod on the boat is angled, the mast has nowhere to go except towards the boat's occupants.
It's highly unlikely, but you know that if it's going to happen, it'll happen to the boat with the broken strap.