Warning about this is airflow, condensation, I would be afraid the moisture outside would destroy my oc or the fans wouldn't work well enough and would overheat anyways
Humidity really isn't a huge issue for modern electronics. Actually, dry air is more dangerous. And that could be solved with a computer fan at the window.
I whouln't replace the existing PC cooling or connect the air pump directly to it. Just something to suck out the hot air behind it. Even just a vent on the desk above the area might work.