According to this article that I found, Wubi "has the side-effect of allowing you to run Linux apps within a Windows environment." I found this statement to be very intriguing: Is it actually possible to run Linux applications on Windows (without rebooting) using Wubi? I know that there are other solutions (such as coLinux), but running Linux applications in Windows using Wubi might be useful as well.
Technically you are not running Wubi inside of Windows, what Wubi does is install Ubuntu as a "virtual drive" and creates a "loopback" when you boot, this allows you to choose between Windows, or Ubuntu.
So in short your answer is no.
No, not really. Wubi is different. It lets you install Ubuntu to an image and boot it natively. When you get the Windows loader, it lets you choose to boot a GRUB within a loopback device. TO run Linux programs on Windows, where they appear as separate Windows, you'll want an older version of Ubuntu(before Unity), or a non-unity distro like Xubuntu, Kubuntu, or Lubuntu, and Virtualbox. When you use Unity, seamless mode doesn't make windows separate.
I think in the past when you installed Wubi it also installs Virtualbox and sets it up to use the same image, so that may be what the article refers to. I don't know if that is still the case, though. It's not really running "in windows", though if you have a non-Unity-based window manager and Virtualbox seamless mode it can certainly appear similar.
The main difference between Wubi and a normal installation is that it installs the linux filesystem to a file within your NTFS partition, rather than making a separate partition. However, you're not "running windows" in any meaningful sense when you boot normally to a Wubi installation. The kernel loads normally, and loads a ntfs driver from an initrd, and then finds the Wubi image and mounts it as the root filesystem (see pivot_root for how it can mount a root filesystem while it is already running)
See also What's the difference between Wubi and a regular installation?
Wubi allows you to install Linux from Windows. Afaik even inside a Windows partition without repartitioning (by using an image file). As far as I understand this is not what you are looking for.
But... you will be intrigued by Cygwin. Kind of the opposite of Wine, but working much better. Cygwin provides Linux API calls in windows and can run almost all native Linux applications (except maybe some very system specific tasks. Cygwin even provides a X-Server and lets you
ssh -X
to a *nix host to see X11 application windows over network.