It can't directly, because it will contain bindings to the SharePoint 2010 DLLs which of course don't exist under SharePoint 2007. However the good news is that most of your work can be kept.
SharePoint Development with Visual Design User Controls on SharePointDevWiki describes how to do the equivalent of visual web parts for SP2007. Have a look at the components explained in that article and you'll see how they already match up with your solution. You just need to repackage it.
If you wish to use VS2010 to do this, know that it doesn't support targeting SP2007. I recommend using WSPBuilder for this purpose.