Well the easiest way is to change the default app for users to your own app via;
http://docs.splunk.com/Documentation/Splunk/latest/Admin/Setupbuilt-inauthentication#Add_and_edit_us...
From here you could select your App as the default. Each time a user sign's in this will be displayed. For a splash screen you are best editing the welcome/login page.
http://docs.splunk.com/Documentation/Splunk/latest/Developer/CustomizeLogin
Finally. You can remove all the links in the top right if you wanted to create a seamless look for your App, you don't even need to have a Splunk logo on it!
Have look here for advanced customization options for the XML.
http://docs.splunk.com/Documentation/Splunk/latest/Developer/AdvancedSearch
If you wanted to run it outside of Splunk, then no. Not at the moment, it requires a browser to access as it is run from a Python based Web Server.
