No I believe it supports PCIe 16x 2.1. A new motherboard wouldn't get you to 3.0 you would still be at 2.1 so there is no benefit in a new motherboard except it's ability to OC your processor further.
If you want a new board then you might as well buy a 8320 or 8350 and the cheapest motherboard that will go with it.
A 8320 is $180 and a AM3+ motherboard starts at $50 just make sure the 8320 is in the supported list for whatever motherboard you get. If you want to do it in steps you could grab a AM3+ board now and the cpu later.
I wouldn't spend much on the motherboard unless you are going to be overclocking. The problem is that the motherboards start to skyrocket in price once you start adding in complicated power deliveries. You can get an MSI 125w capable board for around $50 or if you want something better then grab a GIGABYTE GA-990FXA-UD3 ~$140.
Don't buy unless you are going to get an 8320 or 8350 though. Right now those processors are about as good as you can get from either sides of the fence and that is coming from an Intel fan.