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

That sounds quite doable. When I want to create a new LogicModule I generally start by looking for an existing one that is close to what I want and take bits and pieces to create a new one. Perhaps try looking at DataSource "PostgresServer-" and "Azure_SQLServer_JDBC". These are code-less as they use the JDBC method. There are various examples of other SQL checks which use groovy code but I didn't really find one that was simple to follow if your not a coder. Sometimes it also is useful to look at PropertySources even if you are not looking to create one. They may be simpler than DataSources or Eventsources and you can reuse it's code.