It will most likely run right around 30fps in normal PvE. In very large events or very large WvW it will get choppy and at times feel "unplayable" or at least frustrating. This can be mitigated a bit by switching to "low" but for most of us it still isn't good enough.
My fiancé plays on my old system. It's an E2180 CPU (OC'd) with an 8800GT (OC'd). Looking at benchmarks, this system is comparable and slightly slower than your setup. Most of the time she gets along just fine. There are times she gets very frustrated with framerate during the most taxing conditions with low-medium settings.
Will it run it? Absolutely. You already know you're on the low end so the simple answer to your question is yes.
the pentium G is fine, I dunno about the gfx.
Low is no issue, medium.... eh not sure. may drop frames when a lot is going on. Anyhooo you may have upgrade options for your GPU later. new 650Ti looks great for $150
Maby mid settings and yes large events and WvW is out of the question not because of your GPU but because of your CPU
I have a stock clocked (3.0ghz) Core2Duo E8400.... an old ass 2core. He has a Sandy bridge dual core. I play on medium 30-50FPS PVE, and horrid 10-20 WvWvW. The Pentium G is not the best gaming intel offering but it can handle this game without a doubt.