A function can return void and still throw an exception. (Like one I wrote today, "insert row into table", which throws on failure and return nothing on success.)
A bunch of functions that all return void all being called in a row, though? That's a much smellier smell. What happens if their order gets mixed up, for example.
Testing that function would be a matter of mocking out the database with a class that can emulate the type of failure that would trigger your exception.
it's almost more worthwhile than testing your happy path - when things go wrong you want to have guarantees that they'll be handled correctly and not kill your server.
A bunch of functions that all return void all being called in a row, though? That's a much smellier smell. What happens if their order gets mixed up, for example.