Yes that 7850 has 1 6pin and your system should be find. It looks like a decent little setup but is the two monitors and two hardrives neccessary? If they arent i would defenitly pick up only the 24" and the 1TB HD and put the rest into a better gpu/mobo/cpu, if this is for gaming anyway.
The system I posted is what I currently have, I added in the card to that list to make sure the power supply could cope with it. One last thing, I had a look around and came across this. I am leaning towards the MSI version I would just like to know your opinion out of these two.
A factory overclocked 7850 would obviously be better than a stock 7850 however personally i dont like gigabyte cards. Not saying they are bad but i have never had luck with them. If i were you i would just stick with the stock MSI 7850 and OC it from there if you desired.
That said your system looks like its probably due for an entire upgrade soon, if you had the money that is.