Yes, you can absolutely build a protective hut for your Mammotion mower and situate it against a side wall to shield it from bad weather. Many users do this to provide extra protection from the elements, and it's a good idea to position it so the opening faces away from the prevailing wind and rain.

Just make sure:

The hut has adequate ventilation to prevent moisture buildup
There's enough clearance for the mower to enter and exit easily
The GPS/RTK signal isn't obstructed (though against a wall should be fine)
The charging station remains accessible and functional