pylon:
Can I capture it as asynchronous data then?
Yes, but for an asynchronous serial interface you need to know the baudrate. Do you have that?
Guess this would mean that I wouldn't need to worry about software SPI for the display.
Correct. In this case you can use the hardware SPI for that purpose.
The UNO has just one hardware UART (which does that asynchronous serial interface) and that one is used for the USB connection. You still can use it in your application but keep in mind that you won't have a debugging possibility over a serial connection.
Yes, I have found that the baud rate is 31250 which seems to be ok for arduino? I'll use hardware uart and just try to manage without debugging over usb. I'll give this a try and write some code and see if I can get it to work 
Many thanks!