Yes, it should be step-free but it's really not at all hassle free with luggage, multiple lifts** with waiting time, quite long walks down various tunnels involved, serious crowds at time, it's really a pretty nasty experience with heavy luggage, compared to getting on a train at Edinburgh, stowing your luggage, sitting down and that's it. If XC worked properly and had enough capacity it would be a far, far superior experience than going via London.
**The chances of at least one of the sets of lifts being out of order are pretty high when so many are involved - is it four or is it more?