Is there a way to grant SELECT for every database (including new ones) at a server level?
Since you do not know the schema or tables names to grant them to, no to specifically doing it. You can add your AD account to the db_datareader role within the model database, and this should be copied into each database created on that instance.

In addition, if databases happen to get created via restore or anything other than create database statement you can use Policy Based Management rules to easily verify if your AD account is a member of that DB role and if not take an appropriate action.