can a gaming psu handle voltage fluctuations?

As long as your PSU can handle the wattage of the highest power drain its fine.  THat should accept it fine.

One thing people getting a pc don't consider is the PSU, if you go upgraidng things then its worth looking at higher rated PSU.  Generally a small fee when buying a PC will get you a better PSU that supports more in future.

They can handle "some" fluctuation.  But there is no guarantee and it does put "wear and tear" on the unit. 

Simple solution.  Purchase a UPS battery.  They make them for home computers in the $40 range.  They have a battery in them.  The battery is constantly being charged from the wall outlet.  You get your power for your computer through the battery and not the outlet.  

So if the power goes up or down, or goes out completely, it does not affect you computer.  You get your power from the battery.  

Think of it like if you are using a laptop that is plugged in, and the power goes out, you laptop keeps working because it is connected to the battery.  A UPS does the same for your PC or game console.

That's a problem with your building's wiring, not your local electric grid. All (decent) power supplies should handle the occasional short brownout, but if you want to be on the safe side, get a surge suppressor or UPS.