Skyrim is better balanced now than it used to be after the updates so dont worry.
No you won't be bottlenecked much if at all. Enjoy your new build, and as always happy gaming
no i played it on an oc'd q6600 3.5ghz only a few months ago with all the updates, and it runs insanely better with an i5, and that was with a 6850 i had at the time which is very similar in performance to a 7770.
You can grab a cheap cooler like the Zalman CNSP5X for about $10 and then OC the 8200 to about 2.8ghz and reduce the bottleneck (only works if you have ddr2 800mhz or ddr3 or higher spec ddr2 since in lga775, mem speed is tied to fsb and oc is via raising fsb and any higher oc will run ram[esp ddr2 800, ddr3 any/ddr2 1066 can go a bit higher] out of spec)
there is a follow up reviw where they OC the q6600 21% for 16% fps gains in cpu limited titles
sidenote: the number of games tested is a bit low and there are other reviews that have slightly conflicting results (due to game differences and different parts of games being tested)
I think as said before games that aren't CPU bound you will do fine with and games that are more CPU bound that play more efficiently with a quad core you would see more steady declines in performance that you wouldn't have otherwise encountered.