The switch on a push/pull is independent of the pot, so you can use it to turn the overdrive on and still be a tone pot. But the depth of the body may limit you as to where you can fit a switched pot, as you need to be able to get the shaft through the hole, which will require some angling in some positions, but you can only angle a pot so much before it won't then pas sup through the hole.

As overdrive is something you'd probably want to switch ion and off mid-song. I'd think about getting a push/push pot instead, as they are so much easier to operate quickly.