Short easy answer: Yes
Long slightly technical answer: Yes
this is because your GT9800 connected to your motherboard via PCI-E 2.0 x16. The HD 6870 uses the same albeit 2.1. You should still be able to connect it to your monitor using your existing monitor lead and see a big improvement in visuals.
I'm kind of going through the same thing. Been meaning to do a total system upgrade for the past year and it took my graphics card (GTS8800) failing for me to make a start. It lasted through 6 years of intensive gaming but now its been laid to rest. Time for a nice new R9 280X I think.