It's a cool idea, I'm not really sure what implications it would have.
In what situations would it be used in a real game?
Well it could either be used when you have a detachment about to die from ranged fire or summit. Join them to your parent and loose the pts, but you still have the models left.
Or you can use it if your parent is in combat to gain steadfast. Maybe the terrain on the table makes the detachment obsolete (you can't fit it in. Join the parent.
It's not widely or universally useful, but I think it'd be a neat trick to use at times.
Can you join a unit that is already in combat? Can the unit that gets's joined still move that turn?
yes, but models must be added to the rear.
As for movement, let's say no (not after a join, but the parent may move and then get joined). So you are better off moving the parent before joining the detachment to it.