SQL Server Backups using Volume Shadow Copy

Short answer: they don't play very well together unless you've got SQL server configured appropriately (and even then I wouldn't recommend it).

There's a lot of information about VSS & MSSQL playing together here:
MSKB919023: SQL Server 2005 connectivity and Volume Shadow Copy Service (VSS).

One word of warning though:

presumably the SQL Server data format is robust enough that such a snapshot would be guaranteed to be consistent and usable

That's a big assumption, and one that's not always safe to make unfortunately. That's why your MSSQL maintenance plans are essential to ensuring you can recover from disasters.

You never backup MDF and LDF files.

You run backups (plans, SQL, SMO, whatever) then backup these backup files.

Frankly, I don't get a fig what any vendor says about VSS. I also dislike any vendor that has a SQL Server plugin for backups. You use SQL Server native backups only

FYI: you also exclude MDFs and LDFs from virus scanning too.

If you don't have software that has a SQL "option" then:

Create SQL maintenance plans or scheduled Backup jobs for the databases, dump them to disk, then backup the server. Or when you dump them, dump them straight to your disk-to-disk backup location if you have one.