Ah memories of doing similar for my N64 and overheating third party expansion pack(in some cases also sticking a bag of ice on the thing) .
Basic physics will tell you the amount of/rate of heat transfer is proportional to the difference in temperatures between the things in question. Related to this moving air can also change things (there is a reason temperatures on recipes will be different for fan assisted ovens), though how much a little house fan pointed vaguely at a closed console will do on that front is a different matter.
This is more likely to be in the domain of the former. As the fans in most consoles are small (you only have the height of the console to stick the blades in) and tuned to reduce noise rather than sounding like a plane taking off (see early xbox 360s), with the console makers mostly caring to keep failures just outside warranties (5 years or so in most of Europe) and also avoid another Red Ring of Death rather than having it work for decades then air flow will be reduced. Big house fan is way larger, people expect a sound from them (which is also less owing to being larger and thus spun slower) and so will direct a stream of presumably cooler room air into the console's path which will take that in rather than potentially recycling the air is just exhausted at a higher temperature thus reducing efficiency.
Where it might make life harder is if people kick it like it is the 1980s and keep things in tight boxes under the TV (we will assume no glass front for this). If your fan instead blows into that and maybe serves to keep the hot air in there cycling round rather than what little transfer does happen then fun ensues.
As far as external fans then the main trouble is when people install them incorrectly. For instance wrong location or wrong way around and turn for want of a better term a suck fan into a push fan, or indeed do that for both parts and stop as much air from getting in and getting out. Other times if the fans are too slow/don't direct enough air through and serve to reduce what was already getting through. How well given replacements do I don't know as I have not tested them or seen them tested for the PS5.