RC159,
I don't have Conexant myself, but compiled & installed modem driver on friend's Inspiron8200 (Conexant based built-in modem) without problem... If I can recall it right now exactly, but remember it may have not been accessible under /dev/modem or similar usual device, but rather a different device.... you should check out the readme which came with your driver (I assume you used rpm package, right?), it should be mentioned there as which device it will be. Then you just would input that device name into the dialer you'd be using.
I use myself SuSE with KDE3; not a big fan of RedHat & Gnome, but the principle is the same.
If you would still have problem to find it and access it, you may wanna try to remove the package and install it from sources instead (compile & install). Also, make sure you have the correct package (either rpm or tar sources for your version of Kernel)..
good luck!
dave