I doubt that any tub overflow will keep up with a free flowing tub spout.
Normally there is just a small slot that allows water out.
The overflow will give you "some" cushion for error though.
When I get calls for leaks under tubs, it's sometimes the rubber seal between the tub and the overflow. I ask, who used the tub last when you saw the leak?
It tends to be either kids filling the tub all the way up, which would be fine, if the rubber seal was in place and working.