Your assembled board will likely be missing connection between some of the BGA balls and the board. That's almost as bad as having a cow step on it. If you are putting the via IN the BGA pad, your only choice is to have the vias filled and plated over at the board fab house. There are many reasons you shouldn`t use via in pad. It`s not good practice, and those via holes act like little capillary straws and suck solder off of the pad or the BGA.
That said there are some applications that may require, or seem to require, via in pad. Here are a few examples of why you might need to use via in pad:
So if you don't have a choice, here are some methods you can try when using via in pad:
If you're putting the vias between the pads, you have two options. You can put soldermask dams on the short trace between the pad and the open via. This will prevent solder paste from migrating. The other, and better, option is to cap the vias with solder mask. This gives a bit of extra protection in case any of the solder mask dams are too thin or chip off. Just make sure you cap these things on the solder side. If you cap them on the back, solder can still spread on the trace and partway into the via. That still puts the electrical and mechanical connection at risk.