The cast is likely self-supporting, although the flange should be anchored to the subfloor. Unless you remove the flange then reinstall, you'll have to cut the subfloor so that it can be slid underneath the flange. Blocking to support the ply edges is highly desireable.
If you are thinking of tile which would raise the total floor height, consider either removing the flange or cutting off a chunk and replacing it all with pvc so the flange can be on top of the new FINISHED floor where it is supposed to be.
Unless that arm holding the flange is very long, it should be quite rigid. If you have any trepidation, you could install a hanger to hold it prior to cutting out the subfloor, but it normally wouldn't be needed.