You can, but if your solution is at all like theirs the onus will be on you (what-ever legal team you can afford against their 800lb gorilla) to prove that you didn't copy it.
It is far safer not to look at all, and IIRC ReactOS's developer guidelines prohibit their devs from doing so for the avoidance of doubt.
> or write documentation about the behavior of the APIs and general behavior.
What Compaq did to implement the behaviour of IBM's BIOS (the only part of the original PC that wasn't off-the-shelf) was to double-clean-room. Two completely separate teams were on the job: in one "clean room" they analysed the chip's behaviour in detail and documented everything significant, and in the other a team implemented a design that mimicked said behaviour.
I doubt the ReactOS team have the resources to properly pull this off for something as large as the Windows source code though, and even if they did that still wouldn't get close to their target of Win2003 & later compatibility (there have been some significant changes to parts of the driver model since the XP days).
If though, you're asking if they "can" in very generic terms, yes, certainly - as a matter of fact, this has been a large controversy of ReactOS.
There are no certainties, as everybody has their own side of the story. An MS developer, Axel Rietschin, publicly expressed his opinion that there are wholesale ripped off (low-level) functionalities¹; I personally find it convincing, although it's fuzzy, as he doesn't give details.