It's absolutely how you get a pet!

The creature drinks its fill of the water and then burps, licking its lips afterwards like it didn't just make an undignified sound. Looking at Vash with big white eyes, it chirps again and then climbs up on him, scurrying over his shoulder and settling around his shoulders like a big feathery scarf.

Did... did it shrink a little, too? Just enough to not be too heavy? Maybe.