That would be pretty straightforward, and it certainly wouldn't hurt, but I wonder if its overkill.

The deck will be Doug Fir 2x10's. Screwing a 2x10 to beams with three #10 screws at each end (>1.5" of relish) gives ~500 lbs of lateral (tension) load. There will be five rows of 2x10's, laid side by side, going out from tree...giving something like a 2,500 tension load.

Do you think that such a properly-screwed-on decking will itself serve as the tension band?