No. It's screwed up buck/doe ratio in some area's that can cause late dropped fawns.
This is where APR's should help.
If anything, we shouldn't protect late dropped fawns, since the late dropped fawns will be what comes into heat later in the rut, thus continuing an endless cycle of late ruts/late drops. We'd be better off to shoot as many late dropped fawns as possible and then hope a bad winter takes the rest, to set things back to right.
A September season makes it easy to identify button bucks from a young doe, so less buttons will get killed if you fill an antlerless tag in Sept. vs waiting until December.
One must also keep in mind that hunters in KY, OH and WI deal with any fawn issue and it's much hotter in OH and KY in Sept. than it is here, yet their hunters at least get the option to bowhunt in Sept. While afternoon sits would be warm, a mid-Sept morning hunt could be very pleasant.