Short answer: Yes.
Medium answer: That would be a near-complete rewrite of the project, since the ReactOS kernel and Linux have nothing in common. Different architectures, code styles, conventions, APIs, ABIs (which is super important for drivers). Probably the best option would be to port all of the ReactOS userland to run on WINE (which would actually be cool, and might be easy), and possibly write a Linux kernel module that provided a NT-compatible driver ABI (which would probably be hell to write, but if it's even possible then it would be a huge boon to Linux hardware compatibility... probably).
Yes, only userspace code would be reusable with a linux based kernel. Might as well start from scratch.
One more option that's being tried is to split the difference by integrating more of Wine's code. This approach is being testing in the Arwinss branch[1]
NDISwrapper, Captive NTFS, Linuxant? Sure none of them implement(s|ed) the whole interface, but it shows that it is far from an impossible task.
Or as I like to call it, 'using'.
But that's not dogfooding. If you were a ReactOS developer using ReactOS to compile future version of ReactOS, then you would be "eating your own dogfood", but simply using it as a daily driver doesn't count.
If you'll search through ReactOS codebase, you'll definitely encounter Linux pieces of code, thus it's safe to assume ReactOS doesn't suffer from NIH syndrome and that it salvages whatever it can from any given legit available source. Other than that, ReactOS has its own NT reference (which covers stability too) that it has to follow and that isn't any of the easy-available *nix architectures, so there's that.
That said, the last three times I've tried dogfooding ReactOS, I had trouble keeping it stable for more than 20 minutes, which is a complete non-starter for getting non-technical people using it.
It seems like the people working on the project are very smart and motivated, so I have to wonder why this is still a huge issue? I know almost nothing of OS/Kernel dev, so is it basically impossible to salvage all the stability work from the Linux kernel?