You can't do that. I mean of course you can do that but it makes no sense. Either you will be sacrificing CPU performance or GPU performance and that will eventually come back to bite you. http://www.anandtech.com/bench/Product/102?vs=288
shows you the performance comparison of the quad core AMD against the 2500K. As you can see in the gaming tests the 2500K runs away with this test. This will benefit you with games that are generally CPU intensive. Then again there are games out there that are more GPU intensive and having a beefier gfx card would be key. I mean 1st off you are going to be playing @ 1080p off the bat and with a 1GB card you are going to be struggling in any event. With a 1.2-2GB card the performance would be a LOT better. Higher VRAM for higher resolutions. A system needs to be balanced. If you haven't bought the parts yet do yourself a favor and learn some patience. It took me 8 months to buy each component for my computer. I was not about the make the choice of where do I want to screw up my computer. I could have easily afforded a GTX 460 or something. However with some patience and saving money I am the proud owner of a newborn GTX 570 Classified. He is already running at an average of 100FPS in Crysis with Nature mods and well over 100FPS in every other game I throw at it. He was weighed before he was shipped and was nearly 3 pounds. I couldn't be happier. So ask yourself can you be patient and reap some SWEET rewards or do what I used to do? It's my money and i WANT TO GAME NOW!!!!! You are making a conscious decision to sacrifice performance when in reality if you just wait another month or so you can save up money and climb the performance ladder until you can afford the 2500K & a beast of a gfx card. None of us like to wait but with age and maturity we learn to invest our time and money more wisely to optimize our returns. If I had only saved for two months I would not have anything close to what I have now. I built this beast and I wasn't about to settle.
As far as HD streaming you will want a min. upload of 2mbps to stream with some good quality. Most likely more if you are going to be streaming your 1080p gaming live. This will call on your GFX card heavily to display the awesomeness for you and to stream it for everyone else as well as your CPU because of the virtual cam/streaming program like FME or VLC or whatever and your gaming.
Intel Core i5 2500K @ 3.30GHz29 °C
Sandy Bridge 32nm Technology
8.00 GB Dual-Channel DDR3 @ 665MHz (9-9-9-25)
MSI P67A-G43 (MS-7673) (SOCKET 0)33 °C
DELL 1704FPV (1280x1024@60Hz) Upgrading to TCL L40FHDF11TA soon
1280MB GeForce GTX 570 Classified HD (EVGA)35 °C
78GB Western Digital WDC WD800JD-00MSA1 ATA Device (SATA)29 °C
977GB Seagate ST31000528AS ATA Device (SATA)28 °C
ATAPI iHAS124 Y ATA Device
Realtek High Definition Audio
That costs about $1000. Add in the retail version Windows 7 Professional , Coolermaster V8 Heatsink, my AZZA 2000R gaming case and a Corsair 850W enthusiast edition PSU. I spent a little over $600( read well over TWICE that amount ) for the best gaming I could find where there was a balance with price vs performance. I wasn't about to spend $1000 on a gfx card for 10FPS more.