Did you set the database name in your connection?
Yes, you can connect directly to SQL Azure with a PB application. You CAN use OLEDB even though they say it isn't supported. Make sure that you open up a port in SQL Azure - 1433 if you are going to run your application on your workstation.
server will look something like this: ablahblahblah.database.windows.net,1433
and then you must provide the database name too.
If you are just running a VM, then you can install sql express or any other sql server that you have licensed. At that point it is pretty much the same as rackspace.
SQL Azure is nice since it has many enterprise features and it also has the auto-backup. The downside is that it doesn't support a sql server backup/restore process. They have added a lot of features in the past couple of years and removed many restrictions.