I'm no USB expert but from what I understand that won't work. I'm sure I'm going to mess up some of the terminology here but the FT232 is used to convert USB from a host controller (computer) to UART level. I don't believe the USB signals from the GPS are coming from a USB host controller. In other words converting a USB signal from a USB device to UART is not as easy as converting the USB signal from your computer to UART.what about connecting the GPS output data to an FT232R, then from there to the uC uart..?
What you could try to do is probe around on the GPS and see if any of the test pads that I can see are actually UART level signals and use those instead.