All loading/unloading processes will stop the ship and if one ship stops, the whole TG stops. Nothing actually happens until the time delay has run out. But in your case, beware of the infamous double-parasite problem, though I'm not sure if it happens with ground units.
Basically, if you have a fighter docked at a carrier, and then that carrier docks at a space station (or whatever), the fighter vanishes because VB6 Aurora cannot handle multiple layers of parasites.
Now, I don't know if that is a problem with ground units, because I've always used separate ships - one is the comfortable troop transporter that does the long trips and another is the fast landing ship that does combat drops, and the ground unit gets transferred from A to B at a planet/asteroid near the target.
I think I've seen AAR's where players have done what you describe but I'm not 100% sure and of course it's always possible that they launch the assault shuttle first, then transfer the marine company over.