Yup, a greeting was something I added to another site of mine a long time ago. Users loved it.
Can't promise anything, but its an interesting idea. It all depends on the theme of the theme...erm...as in what the theme is about.
JPdeni is right, loading another theme requires manual changes to source files - a mod. But making a theme with totally different gfx and stylesheet is quite possible. It only has to check for the time of day in index.template and then load the appropiate stylesheet and set the right images folder. Of course each changed template in that theme needs two sets of "changes". But setting a switch will accomplish that..plus of course not chnaging so much outside index.template.
Or..you could use layers.