Yes, it is possible to use Sunday Keys for MainStage and the Sunday Keys iPad App at the same time with one keyboard, but you will need either two separate audio interfaces or an audio interface that can have the input be blended between USB and Direct sources.
If your keyboard controller has both USB and MIDI 5pin, you could connect one of the Sunday Keys setups via USB, then connect the other via a MIDI cable.
Another alternative, though admittedly more expensive, would be to purchase and use an interface like the iConnectivity PlayAudio12 to route the MIDI to both devices at the same time. One hiccup with this setup is that if using a USB-C iPad, you'd need to insert a hub with PD between the PlayAudio12 and the iPad in order to keep the iPad charged.