There will be a considerable amount of end play as the only thing holding the axle in place is the C-clip that stops it from pulling out snd the center pin that holds it from pushing in

The bearings will be pressed into the axle tube and stay in place until pulled with a slide hammer. They are also lubricated with the same gear lube as the center diff, with the oil seal being outside of the wheel bearings.

As long as you don't have 'lateral' movement of the axle, (up/down, front/back) and it only goes in/out, then you're fine