Why would you want to run the Windows version of QGIS on Linux? Because its there. Actually, it may be a useful way to test the Windows version without firing up the dusty old Win32 box.
I did this more out of curiosity than anything else. I installed Crossover Linux (http://www.codeweavers.com/products/cxoffice) on an Ubuntu Dapper box. During the install process you are given the option to install Windows software. Of course QGIS isn't in the list of supported software, but there is an option to install Unsupported Software.
The QGIS installer ran fine, however there was a problem with the fonts -- they were invisible. I clicked my way through the install, unable to read the options/buttons. Obviously this is an issue if one didn't know where and when to click.
Once installed, QGIS ran fine, although there were some font issues, specifically with the Plugin manager. I was able to load a PostGIS layer, zoom, pan, and identify features.
While Crossover Linux uses Wine under the hood, you can also run QGIS under Wine itself.