The flange should be anchored to the subfloor and should be on top of the finished floor. So, it would be best if you removed that patch, removed the flange, install the new subfloor (IF you have enough length on that CI stub to install a new CI flange), install the new finished floor, then install either that, or a new CI flange (probably need a plumber to do the leaded joint). Or, while the subflooring is up, cut it off, replace with plastic using a no-hub connector to join the two materials, then new plastic from there. If you notch the tile before you lay it in the right place, you won't need to try to drill through it to anchor the new flange to the subflooring. You'll want to replace the shutoff before you're finished, too.