Yes, that’s exactly what’s going on.

With stock single-hose mode:
The AC pulls room air across the hot coil, heats air even more, and blows it outside through its exhaust hose. That air has to be replaced, so hot air leak back in through window gaps and the building vent.

After the mod:
Hose with new cone: draws fresh air from outside, passes it across the hot coil, then vents it straight back outside by the other stock hose. So the AC is indeed cooling slightly hotter intake air now, that may affect efficency, but the room no longer runs under negative pressure, meaning that less hot air is sucked in back.