No. The project has no legal entity in the US.

What about people using it in the US?

I think ReactOS is mainly being used by hobbyists, and I doubt Microsoft would want to sue hobbyists. Little commercial or financial gain, lots of bad press.

The situation is a little bit comparable to Hercules, the IBM mainframe emulator (although not quite the same – Hercules is of course a hardware emulator, ReactOS is an operating system clone). You can use Hercules to run z/OS, but not legally, IBM only licenses z/OS to run on IBM's own hardware, or authorised proprietary emulators that cost $$$$. Thankfully though, IBM doesn't appear interested in suing hobbyists – IBM treats the hobbyist community as if they don't exist. But, try building a business on Hercules, as the company TurboHercules SAS did, and IBM's lawyers will start sending nasty letters to you.