Eh, there is a ton of unrealistic technology in book 1, the stealth ship for instance is impossible. By the authors own words they don't think of the books as being Hard Sci-Fi, harder then Star Trek sure.
What makes you think the stealth ship is impossible? They explain the concept pretty well in the first book: extensive cooling systems to soak up waste heat, large liquid tanks to store that heat internally for a while, and radar-absorbing coatings. We literally have all of those pieces today, it’d just cost unfathomable amounts of money to build with our current technology.
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.
I don't know when that was written, but it definitely feels like The Expanse authors read that exact page and built their stealth system to address those points - the stealth ships in the books aren't permanently stealthy (they have to radiate their heat from the internal heatsinks after some amount of time, seemingly on the order of months), and are immediately detected when they light up their engines (and hence coast until they reach their destination).
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.
Unfortunately for cool space battles, no this still doesn't work for the reasons outlined.
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.
