That's entirely up to the company operating that ICE or TGV train. Not saying it's going to happen - many companies don't let other's wagons on their trains. But many do.
BTW so far my friend's train was never delayed by his own fault, not sure what problem you're talking about - there's no problem, his train had usually the lowest priority (it costs money to have higher priority) so he's the one waiting for "normal" trains.
When I said there are delays, I meant the "normal" trains primarily. But sure, as he increases operation it's going to happen to him too.
Improve schedule planning and Amtrak won't have problems too.