Well, with a dual-core CPU, if there is a bottleneck, it ought to be minimal. Mostly it's the old single-core P4s (and their AMD equivalents) that you'd worry about that with. The RAM and motherboard should not have any negative effects either.
So I'd say the 3850 is going to be fine as long as you have the right power connectors -- the one you linked to takes an 8-pin plug, so double-check you have one of those or at least a 6+2.
Depending on what you're after on the HTPC front, though, you may want to opt for a 4670 instead, because you can get an HDMI output.http://www.newegg.com/Product/Product.aspx?Item=N82E16814161284