Hi,
Yes it is compatible. I also had OSX operating system as the host with 64 windows 7 as guest operating system. Windows virtual machine is working just as it did under Mountain Lion.
I should note that in my Parallels settings on the security tab, "Isolate Mac from Windows" is checked and that is how I have the setting kept. (Sharing files just got too messy for my taste. If I need to share one, I use DropBox).
Before I installed Mavericks, I shutdown Windows and quit Parallels. From there I downloaded and installed Mavericks. When that was complete, I opened Parallels and Windows and everything worked as before.
Hope it works as well for you.