Hi Rick -

When your solder past reflows, it will be scavenged by the via leaving you
with a starved solder connection, if you have any solder connection at all.
You will also develop some quantity of solder globules on the the opposite
side of the board.  I've seen a couple of cases where the surface tension and
gravity effects were sufficient to consume a portion of the balls under the
BGA itself.

This problem with vias in pads has been pretty well known since the early days
of SMT.  Only a blind via or microvia in pad will avoid the problem.  This is
another reason why most of the BGA suppliers provide some pretty good guidance
for designing and hooking up their devices.

Wish I could suggest a solution, but I just don't have one.

Good luck - Kelly

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