Capacitor bank to smooth out current surges
In the end, all of the current must come from the power supply-- regardless of how many caps you have in your cap bank.  What the cap bank will do is average (a.k.a. smooth) out the current over a longer and longer period of time.  Ideally the cap bank would average out the current over a time period that is much larger than the length of a surge.  

If the surge is longer than the averaging period then the cap bank is not really doing anything useful.  

One huge downside to using a really large cap bank is that the inrush current can get very large.  When the power supply is first turned on, all the caps are discharged.  The current required to charge the caps can be huge and your power supply needs to be able to deal with that current.  Some SMPS chips have a "soft start" mode, or will current limit themselves.  

Sometimes you can also put an inductor between the power supply and the cap bank.  This works great for short surges, but can cause problems with longer ones.