The one varible it checks for the endscreen seems to be "ep8_quinn_lewd", which gets set when you (successfully) ask for a threesome with Quinn and Sage. The bench scene should be a direct result of that, but not set any additional variables. So, yes, that scene and the ending are connected.at least one Quinn variable has to matter (probably getting bench scene)
By the way, what I also just looked up:
The whole mess of variables it checks for the Jill option "(not ep7_jill_lewd or affinity == "DIK" or ep8_jill_state == 0)" in addition to whether you're on her path are the same ones that decide whether she rejects you or not. So for all the Jill fans out there: If you get an "Others" option in addition to the "Jill" option, it's already too late. Getting that option means that she'll reject you and you might as well avoid picking her. In cases where she won't reject you, you'll never get the "Others" option.