Hello Ghoshumbue94
This is not possible. The blue GA cannot be used for online services.
Why would you want a SwissPass? There is no need for it unless you want to purchase a bicycle pass or a dog pass, or use the third-party services (e.g. ski tickets).
If you want to purchase class upgrades using the SBB Mobile app, simply create a new passenger (add co-passenger) and select GA Travel Card as discount card.
Kind regards,
Roland