Windows device drivers are not supported by CrossOver unfortunately. This is by design, since we don't have a Windows kernel running(otherwise our software would be a virtual machine like Parallels or VMware)
This means that you'll need a MacOS driver to talk to your USB devices, and CrossOver will talk to them via the normal MacOS way of talking to devices. E.g. USB disks are mounted in a directory, and CrossOver just reads and writes normal files there. A USB network adapter is configured by OSX and CrossOver uses the normal network API. A USB sound card is driven by an OSX driver, and CrossOver uses the CoreAudio API.
In your case I think the main reason why you use CrossOver is because there is no OSX driver. Many devices like yours however are serial-to-usb adapters and OSX can talk to them via a standardized driver. On the OSX side you get a tty device. On Linux this device would be called /dev/ttyUSBx (with x being a number like 0, 1, ...), I don't know what it is called on OSX. You can forward this device to a standard serial COM port like COM0:, COM1: etc in CrossOver. I am afraid however that this will not make your app happy, because it searches the device list for an USB device, nor a COM port.
We are working on creating registry entries for attached devices, so Windows apps can properly find specific USB devices(e.g. an iPod is a USB mass storage, but iTunes won't connect to any random drive). This would also auto-configure USB-to-serial devices. You'd still need an OSX driver to talk to your device, but once that driver is loaded Windows apps will find it. However, this work is rather low priority(we get very few requests for USB support like that compared to e.g. Internet Explorer 8 support), so it will take a while before this appears(I think the timeframe is years rather than months. Currently all this is in conceptual planning stage).