You must have very clean air already if such a puny fan would be able to keep particulate levels within acceptable limits. In winter, my Xiaomi purifier with a quite powerful turbine fan (or whatever those things are called — they're optimized for pushing air through dense filters) is barely able to keep PM2.5 within 5-10 micrograms on max speed (with doors and windows closed). A PC fan would make approximately zero difference, on or off.