SQL Query execution shortcut OR logic?

SQL Boolean evaluation does NOT guarantee operator short-circuit. See On SQL Server boolean operator short-circuit for a clear example showing how assuming operator short circuit can lead to correctness issues and run-time errors.

On the other hand the very example in my link shows what does work for SQL Server: providing an access path that SQL can use. So, as with all SQL performance problems and questions, the real problem is not in the way the SQL text is expressed, but in the design of your storage. Ie. what indexes has the query optimizer at its disposal to satisfy your query?