Yes this setup should work, are you using the stable version of picoscope?
Yes it is possible to decode SPI using the 2204A. I would highly recommend you try the new PicoScope 6 Beta software which has a much improved serial decoding feature. As the current stable version has some serial decoding issues.
Development is has been working fixing and improving all of the serial decoding features.
These features are now available in the beta version;https://www.picotech.com/downloads/_lightbox/PicoScope6Beta
Installing this will not effect the stable picoscope version if installed.
Before you open the serial decoding feature, please make sure you have switched on channel B and pressed the Auto-Setup button. In the serial decoding feature you should then be able to see both channels, they should be assigned to the clock and the data line you are decoding. The chip select is not necessary.
When you return to the main PicoScope screen, you must change the Collection Time to at least 200 ms/div and Number of Samples to 3 MS or more.
You should also set the Trigger to Single to capture the data upon startup of your device as you mentioned. You can then zoom in as well as capture the data in the table below.