As Serge mentioned, yes. However, you cannot modify parts that are GPL (the window manager is GPL) and then close source it. You cannot even use GPL libraries in closed source code. So the answer should actually be, NO as if you close source a major part of the system or desktop, by the time you are in the free and clear of GPL, it will have nothing to do with Ubuntu anymore. Additionally, I believe you need explicit permission from Canonical to use a word like Mubuntu. The question is really complicated. You need to do a lot of research and probably hire a lawyer if you were to do such a thing.
I thought I would update the question because the comments are getting very long on the topic of whether or not you can use GPL libraries in closed source code. LGPL permits this*, GPL does not**. From the authority on the subject gnu.org/licenses/why-not-lgpl.html :
... using the Lesser GPL permits use of the library in proprietary
programs; using the ordinary GPL for a library makes it available only
for free programs.
However, since most libraries are LGPL these days, the OP may not have as hard of a time as I originally thought.
* There are still certain conditions that need to be followed in order to use LGPL libraries.
** There are certain cases where you can use a GPL library in closed source code, such as if the software is not publicly distributed and if using the library is not considered a modification or derivative work (e.g., prelinking).