With CROUTON wine works - at non X86 models not
The problem is to make it work as an app
But there are a lot of GNU apps that do not work as extensions
Qemu would be even better than wine. You would be able to run DOS / MS WOS / GNU/ Linux / or even Android sandboxed
Anyone with the faintest idea of what a Chromebook or Chromebox is would laugh at the suggestion of running Windows programs in ChromeOS. Or even wanting to.
What you can do is run remote Windows programs via remote desktop apps and thus use ChromeOS as a thin client. Or Linux, Mac or any other OS for that matter.
VMWare has announced this solution and I can see a few companies going down this path.
Most criticism of ChromeOS is from people who just don't get it. ChromeOS was never meant to be a general OS like Windows. It is a secure client for the internet or internal network. Google continually add new apps and a handful of offline apps for file management and photo and media management. Beyond that it is all "online".
If that is not what you want then do not buy one.
My Acer Chromebook works very well as a secondary device to my desktop. Everything nicely synced. It updates itself and boots in a few seconds. It is a perfect grab and go device with no effort involved in maintaining it.