My question would be 'why shouldn't it?', because I cannot see any culprits. Easiest thing is to try to convert and see what fails and why. Most problems are not Proxmox related like 'loss of windows activation' and stuff like that. It's more a problem of the guest itself with its running applications. On most guests you have to migrate to hardware as similar as possible to the original one to get it to boot, everything afterwards is guest and application specific, not Proxmox specific.
On the page you mentioned is also a "migration from a live system" section, which you can try as a simple test if everything works and play around.
So, to answer your question:
Yes, but depends on your actual hardware and setup and can therefore not be fully answered with yes.