CRO booking categories are not the same as the
DVC booking categories. With CRO, room assignments are pretty much "Run of the House", which nearly always ends up as a Pool/Garden View at the BWV.
AFAIK, they do not treat cash guests differently than points guests (except no one who books for cash can get a Boardwalk view room as those are reserved for those staying on points).
FWIW, I think it is a mistake to request "Non" anything. Too easy for a room assigner in a hurry to pass over the "Non" and just see the "Handicapped-Accessible". So by requesting Non HA, you actually have a better chance of getting one than if you made no request at all. Better to ask for what you want. I suggest you call MS and ask to change your request to "Need a Tub". The HA studios do not have them.
Enjoy your stay.