Hello @DavidPhillips2,
yes, you are right, it is possible.
The screen/video depends first if it you selected a SAS Home (SASVisualAnalyticsHub) running with Classic (Flash) or Modern (HTML5) mode. In this case, all points to the fact that we speak about Classic mode.
I do not think that, from the Theme Designer, anything else than a swf is officially supported, I also don;t think that it will support device recognition to switch splash screens automatically (only Classic and Modern view are supported through the user preferences). Perhaps SAS Technical Support can answer better this question.
To support more possibilities (change the tipe of object for splash screens, device or geo recognition, etc), the only option is to deviate from what SAS officially supports, and modify the web application itself ( /sas/config/Lev1/Web/WebAppServer/SASServer12_1/sas_webapps/sas.visualanalyticshub.war/ ).
However, a remark: you need to evaluate carefully if you would like to deviate from supported operations. I mean, SAS VA is "just" another web application that follows IT/Web standards, a big and incredibly good one, but a web application. Hence, web developers in your organisation can perhaps support customisation and tweaking. But also, if there is a problem, SAS might not be able to support future issues. It is a hard decision that can only be made by your company.
My personal advise is to not deviate from supported operations, especially if you have any doubt.