Short answer: Yes.
Long answer: I was getting the driver warning on the login screen just as you described in your previous post. I believe that when I installed ParagonChat, it changed the DriverCheckLastDate value to 0 because I have all of the registry settings in the CohBeta key backed up, and that value was dword:4c0d874c before.
After I started using ParagonChat, I no longer got the driver warning. So I looked at the registry settings and that's when I noticed the DriverCheckLastDate value was dword:0. Perhaps the reason why it changed for me and not for you is because your registry settings are under coh instead of CohBeta.
Anyway, changing DriverCheckLastDate to 0 should get rid of the driver warning. If your worried about it messing something up, just export the entire coh key to a .reg file from the File menu in the registry editor. Then you can just import the settings if something goes wrong. I doubt that will be necessary though. You're only changing one value and you've already noted it in your post.
PS. I don't know if doing this will help the OP because as was previously mentioned, the driver warning isn't known to prevent the game from working at all. But there's nothing to lose by trying it.