It depends on whether Oracle "respects" AD and trusts the AD user under which Tableau Server is running. If it does, yes. Run As User will work. If no, it won't.
To be positive connectivity will work for you, you might just want to consider embedding an Oracle username/password in the connection that you publish to Tableau Server - that way you don't have to rely on Oracle "honoring" AD authentication requests AND that the RunAs user actually has perms inside Oracle itself.
Thanks so much for the response. That really clarifies everything and I might try to do your suggestion of embedding the username/password of the Oracle database.
That would make it work I think on our end just because we don't control the Oracle database and setting all that up on their end might not be feasible.
Thanks again for your suggestion!