Err... no. Not unless the installed base reaches a critical mass. And certainly not when the market share is not even 0.1%. macOS (or even desktop Linux) has a higher installed base and they don’t bother Microsoft significantly.
I’d be more optimistic if the OS had not been around for two decades. It had its chance when the likes of Vista was released. If it didn’t make a dent back then, it is not going to make one now - especially since Windows is at its best in terms of usability. Sure there are concerns about privacy, but those didn’t prevent Google from acquiring a (almost) monopoly in mobile market. Microsoft’s own attempts went nowhere — and they have infinitely deeper pockets compared to people behind ReactOS.
And even if it does gain momentum, I am fairly sure that Microsoft will find a a way to sue them into oblivion.