Is it possible to directly query the SQL database to find the installed module(s) and their version?

You can use the OrionServers table. 

Note that it will list all the sub-modules/features so you can ignore some (Cloud Monitoring, NetPath, etc). You can compare it against your modules you have licensed in the Licensing_LicenseAssignments table (ProductName column).

And easier approach might be to go to the bottom of just about any page you go to in your environment, you should see a list of the modules there?

Yeah, the intention here is that all servers are gone, and we're in such a worst case scenario that the only think we have readily available is backups of the SQL databases.

This is perfect, thank you.

To share what I ended up with, here's the MSSQL query that returns everything needed (I hate using SELECT *, but there really shouldn't be too many rows in these tables, and it makes it simpler):

SELECT * FROM [SolarWindsOrion].[dbo].[OrionServers]
SELECT * FROM [SolarWindsOrion].[dbo].[Licensing_LicenseAssignments]

With just this query, and a little bit of manual parsing of the "Details" field out of the row(s) in OrionServers, you can figure out what version(s) were installed on what server(s).  All's that is needed is to first restore a backup of the SolarWindsOrion database somewhere that can run it.