@palamedesAs to moving tens of thousand soldiers, heavy equipment, and fuel literally around the world I think we did a pretty good job during WW II doing just that.
Yes, and in an era of satellite based intelligence gathering, movement of all that shipping would have been noticed not long after it left port, and with it taking the better part of a week to transit the Pacific "on a good day" that gives a lot of time to respond with a counter.
Yes it can be done, the Untied States continues to demonstrate the ability to continue doing it. Doing it without being detected? That's a much bigger challenge. The United States at least has some room to maybe pull it off because it would only be a slight deviation from "normal operations" in a lot of cases, at least depending on scale.
But for China? That wouldn't be anything close to "normal operations" by a great many miles.
The smallest cargo ship can carry 100 shipping containers and the biggest carries over 18,000 shipping containers I would think there is room for more than just the crew of the ship and as for protection what would stop them from mounting a few surface to ground and surface to air missile launchers or some other type of defense.
Oh there is
room for the troops. What there isn't are
facilities for said troops on those ships.
The engineering plant for the Ship is designed to meet the electrical needs of the ship and not much more.
So any electrical needs of the embarked troops beyond that? They have to bring hose generation capabilities with them, and the logistics tail associated with that.
Any other "hotel needs" (as I previously mentioned, food, sanitation, water) are likewise going to need to loaded onto the ship as well.
So now you have a transport container(or more) full of "mogas" or some flavor of aviation fuel if not both to supply the troops with power generation capabilities while at sea, and for their assault on the United States once they've arrived. So you're probably talking about a lot more than just one or two, armored combat vehicles aren't renowned for their fuel economy, if anything, they're renowned for their ability to consume huge amounts of fuel in short distances. If they're bringing helicopters along, they'll need fuel for them as well.
Of course, the logistics of moving a helicopter in a RO/RO or even in a sea-can is even more daunting, as there is going to be "some assembly required" before they can be used again.
Even for the Maritime prepositioning force assets that the US Military uses typically takes
several days upon arrival to be brought up to "operational" status. And we fly our guys to where the ship is making its port call for unload.
At least based on my Amphib experience, a 20,000 ton amphib is going to bring about 600 moderately armed(they have heavy vehicles/weaponry with them) infantry forces ashore.
A 40,000 ton amphib can bring that count up to about 2,000 moderately armed troops(by itself) with some air support thrown in.
Which is the other part of the problem with "China invades using Cargo ships only" they're going to be invading without air support. That's asking to be turned into mincemeat by the Air Force and the Naval Air Wings. Even if they somehow managed to get a beachhead, there is no way they'd be able to hold it as they get bombed into oblivion.
It would be a very short lived invasion. Even if they managed to capture a major airfield on the Gulf Coast, they'd be sitting ducks while China tries to figure out how to get fighters there, as they don't have the range to get there in the first place. China has no means to refuel in flight especially near North America... And they'd still need to fly across either the US or Mexico to get there, and if the US knows it is being attacked, Mexico isn't really going to wanting to authorize Chinese overflight of their territory. Which means either the Mexicans try to shoot the Chinese down, or they let the USAF enter Mexican airspace to do it for them. In either case, their air support either crashes(ran out of fuel), or gets shot down before getting to the Gulf of Mexico. In either case, they're still invading without air support.
If they brought the carrier around, it makes it near impossible for a surprise attack to happen as we'd notice it is in Caribbean long before anything happens, and the state of their (manned) Jet Fighter carrier aviation program is rather sad. Odds are very good they'd be shot down quickly, after which we're back to "no air support."
But restricting ourself to RORO ships, the largest RORO ship was built by Japan, and has a dead weight in the 41,000 ton range and max displacement of about 75,000. Considering that they'd be inefficiently providing "hotel services" in terms of weight and space, they'd probably not be much more capable than a Amphibious Warfare ship for troop and material carrying capacity. Probably less all things considered by we'll say it's slightly better than equal.
The problem is RORO ships are limited as to where they can load and unload from, and need pretty specific port facilities to operate. (It's why the US Navy's Sealift Command has yet another class of ship to help provide exactly those services to its own RORO fleet should the need arise)
Which means China has a bit of a chicken and the egg problem then. They need to reach a port in the United States which can accommodate a RORO ship, do so while
undetected and unload/seize the port before US forces can sink/seize the other
unescorted ships in the invasion force. They have further headaches to deal with from there.
China might be able to mount an amphibious assault from a RORO ship, if their troops brought the right equipment along. But knowing what I know about "welldeck operations" I certainly wouldn't want to be one of the troopers who drive off the end of the ramp while
many feet above the water. I wouldn't expect those soldiers to be combat effective after such a plunge.
Even our very dated AmTrac's were normally at least partially in the water before driving off the ship's stern gate, and they
knew when they hit the end of that gate(/ramp) because they suddenly drop like a rock before bobbing back up to the surface. It's not a very gentle experience even then, and Marines getting injured during training exercises is very common even in those conditions.