If I remember correctly, some units used to do this. We had an enormous window unit and it had a large knob, when cranked some louvers opened up to the outside and sucked in air, when closed it ran the air past the cooling coils. I believe the same knob, or additional switches choose the cooling unit or just the fan. This was over 40 years ago so I may be mistaken. We lived up north and had to pull the unit and store it every fall because it could not be sealed up properly and would leak air - as most units did.

I suspect that few people used this feature, perhaps because it leaked air a lot even when closed, those louvers just did not seal well and the outside opening had a screen across it that got choked up with bugs and dirt and had to be kept clean. And of course there were the goof that opened the louvers and also cranked up the AC unit itself and then complained it was not cooling properly.

If this is not available on any units now then it would be cheaper to just put a box fan in another window when you want the cooler night air to circulate. Better yet, a whole house fan to suck the air out and pull th eair in through any window that was open.