Yes you are correct. So called winmodems do not have a controller onboard, but are designed to operate off the motherboard's resouirces. They are made for, and have drivers for Windows. Without knowing what the exact model of the modem is, it is difficult to say if there is any posibility of it working in Fedora. If Fedora did not pick it up, then it is likely not going to work.
For someone starting out in Linux, it will save a lot of headaches if you go out and buy a hardware modem. They are harder to come by, but worth the effort. Most external modems will work. Look for modems that do not say winmodem on the box, or that state that they work in Linux. If you buy one at your local computer store, ask a salesperson, telling them you need a modem for Linux. That way if it does not work, you can easily take it back.
DapperDan has had some luck in this regard (finding modems that work). I have not used one in quite some time.