To my knowledge SQL Audit will capture ad hoc queries, parameterized queries and stored procedures. It just doesn't keep the values that are passed to parameters. This is the same for stored procedures, not just parameterized queries. If you want to capture every single value passed, you can just use Extended Events to capture the queries made to the system. You'll have to be prepared to manage quite a lot of data, but it's easy enough to capture all everything if that's what you want. You could also look to enable Change Data Capture in addition to SQL Audit if you really want to see each and every change.

The audits I've had done in the past didn't require us to capture all values passed to the database.