Can LM run a SQL Query against a specific Server/Database and alert based on the results?

If you look at some of the Microsoft_SQLServer datasources, this seems pretty easy to accomplish. I would say, look at the Troubleshooter one. Clone it out, and see about playing with the code to make it run what you need. The Active Discovery script looks pretty simple to alter to your needs. Add in your select and do a check if its null or empty string.