Summitting Katahdin after October 15 without vehicular support, when the days are short is possible, but it's not the way most would prefer to finish.
Make the effort to reach Baxter State Park before the 15th when waiting for the weather is less apt to be an issue and campgrounds are open. Better still, plan to summit by September 30 unless you are able and willing to wait for an opportunity to summit.
At some point, depending upon the weather, Katahdin trails close for the season until such time when they reopen and winter rules apply.
Click on Thru-Hiking in Baxter State Park, strike [PageDown] several times to read When can I hike Katahdin? and learn about issues associated with October summits.