how much height does this add to the graphics card?

it don't add to much height maybe 1/2" but, the issue is the fan and cooler needs to be mounted or have room in the case to mount.

The compatibility list shows "GTX 980" I have a GTX 980 FTW, which is slightly modified from the reference board. Does anyone know if it will work?

I am not sure.. I can tell you that it also says it would work on the 980 ti and it did not work at all with it

Hello would this cooler work for evga 980ti 4996 version?

According the manual: https://www.arctic.ac/us_en/downloads/dl/file/id/1931/accelero_hybrid_iii_120_installation_manual_english.pdf It should, however the HS were made for the reference board design. So if your card has been modded by the MFG, then it could be a crap shoot.