Automatically open application

This should be possible. One way off the top of my head would be to have a VS with an Access Policy that performs a login to your Salesforce URL. On that VS, you would have a VPE policy that checks for the user's credentials (and other necessary checks) and then does the SAML call out to Salesforce as the default action. I've done a similar exercise with Google Apps.

I've been wanting to look into this as well, so I am signing up for a trial with Salesforce and will give this a shot.