murphy's law dictates that you'll start some nice plants but then right before harvest time you'll show up one morning to find the lot completely cleared by builders getting ready to start... :)
nonetheless I think it's a neat idea and will keep an eye out for revoluationary radishes and "guerilla" green beans.
Why not chat with a neighbor who does get a lot of sun and look into a community garden project? That way you know your tender basil will stay safe from the bulldozers.