UART as logic analyzer?
There's more to serial than just the baud rate.  RS-232 is a framed protocol.  That is, each byte of data is framed by identifying markers - namely the start and stop bits.  Only when a valid RS-232 packet delineated by these marker bits has been detected will it be sent to your laptop as a valid byte.

Unless your unknown data stream happens to be RS-232 in its format the FT232 chip won't be able to identify valid packets and thus won't be able to tell you what's going on.

There are other FT* chips available that can work with arbitrary data streams or raw IO pins, and you may be able to find a chip that is a suitable match, but finding one in a simple to use dongle may be more tricky.

You really want something more generic, like a Bus Pirate, but in fact anything which is able to inspect the state of digital signal lines fast enough and convert that into a form the computer can read (USB) would do the job.

I often use a generic microcontroller based board to do the job (I use 80MHz PIC32MX or 200MHz PIC32MZ chips and the chipKIT platform mostly).  These boards have the advantage that you can use them for other things as well.  Arduino is popular, but the low end ones may be a bit slow for reliable sensing without using fancy tricks (interrupts etc).