Yes a 3850 would be a great buy. UT 2007 is GPU limited not CPU limited. That 3200 is just fine.
Most people here have way to much time/money on their hands.
What they should really be asking is what is your desktop resolution.
If your @ 1024x768 an older 7800GT or 7900GT would be fine. The 7800GT performs about the 8600GT level. I should know I have 4 systems and that the cards I had and passed down. My card is the 3870 and it works well @ 1680x1050.
My daugther has a 3800 X2 and 2 7600GTs in SLI. Works well for her in UT2007. Shes @ 1440x900 on an LCD.