GPE by itself won't synchronize with Google Calendar, however if you install Erminig alongside, you will be able to bi-directionnaly sync GPE and google.

Erminig: http://code.google.com/p/erminig/ (look at the documentation: well done, with step-by-step instructions for installation!)

GPE + Erminig is really are really excellent together! (congrats to the respective authors )