You should read the getting started docs for information about the build convention and solution naming.
And Yes, you can create a single git repository with separated solutions for the sites you want share the same code, just remember to setup a solution for each web application with the same name of the "slug" of the appharbor application.
For instance:
app1.apphb.com => app1.sln
app2.apphb.com => app2.sln
@alastairtree, Currently, AppHarbor doesn't support submodules, so, we must use subtree instead.