Hello Dan,
If you have SharePoint 2013, then install EM4S 2013 3.0.x. Although, the "Test-SpContentDatabase" command is not required to validate a database against a given web application. This command can be used with any post SP2 2007 database or with any SharePoint 2010 database. The insight gained will essentially reveal the WHAT IF errors and warnings associated with upgrading the database without making changes to the database. The database itself need to be part of any farm and simply needs to be online in SQL.
As a recommendation that to always run test-spcontentdatabase on your 2010 farm before adding ANY content database to your farm despite the version. Even if you can spin up a 2010 instance you should run this command even if you�??re planning on using in-place upgrade. This insight is invaluable and is NOT the same as what you�??ll get out of stsadm �??o preupgradecheck.
This stated, the official workflow to upgrade Esri Maps for SharePoint should be able to upgrade MS SharePoint first and then upgrade to Esri Maps for SharePoint 2013 3.0.x. I hope this answered the inquiry