'allthumbs'; as a long time residential renovation contractor, my very serious concerns would be for the imperviousness of the interface between the tub and the wood decking.
In a standard installation, the tub would be top mounted over a waterproof surface, be it tile or marble, with a silicone seal at the joint.
I'd question whether the technique you're suggesting would satisfy your local building code (?). When it comes to bathrooms water is not your friend!
Please give it a some more consideration before you commit to the hole as you described. It's a very expensive condition to rectify, after the fact.
Cheers, and good luck!