Last tested: Jan 16, 2019
Chat tip: as of 5.12 you can have parameterized connections with PDTs, as long as you use the PDT Override feature and you're parameterizing via user attributes.
In Looker 5.12 we gave the ability to have a special PDT database user that is different from the Looker database user. The PDT user would have different database credentials, and would thus not be affected by parameterized connections.
More on this feature in docs.
Note: BigQuery's "Max Billing Gigabytes" can be set to a User Attribute and Persistent Derived Tables can still be used without the PDT Override feature