They'd need refuels every stop though. Like with early coal fired steamers back in the day.
I got a funny feeling that without much better genetic muckety muck, the hard limit will be the human organism itself. Someone will get to the stars = if we don't screw everything up - but the someone won't be human, or maybe nothing like human.
[1] I know in emergencies they pull mad g, but it doesn't seem like something they keep up for long. Would still burn through their deuterium in no time though.
[2] Like, within an order of magnitude or two.
As a bonus, they even talk about the radar-absorbing coating not being perfect, and being able to detect the stealth ship as an object a few Kelvin above the background radiation when they pumped their radar into it.
https://www.projectrho.com/public_html/rocket/spacewardetect...
The main characters also manage to find a stealth ship after coming across coordinates to it - it was parked and completely offline (and unmanned) in the orbit of a small asteroid, which would further obscure any signature it might give off.
First off you have to remember that when a ship turns it's engine on it's going to be visible effectively to the entire solar system unless there is a planet or something in the way. We already have the capability that we would notice a ship moving in the asteroid belt from Earth and in the Expanse it's going to be even higher. So everyone already will have known when you turned your engines on and can run the calculations to see where you are while you are coasting, so even within the confines of the fiction that shouldn't work.
But let's ignore that and say that for some reason no one was looking when you turned your engines on. Assuming your ship is somehow running with all systems off it's going to be roughly 300 C hotter then the vacuum around it, even with a heatsink like you mention (and a heatsink that can store that heat for months is also unrealistic) you're going to be sticking out like a sore thumb to any infa-red. You're just too hot.