SQL Server Automatic Tuning (for query plans) vs. Availability Groups

In SQL Server 2017 (and up), for a database configured within an Availability Group, with query stored enabled, will automatic tuning work on the read-only replicas?

I don’t think so, because query store data is stored in the read/write database, gets copied to all AG read-only replicas, would thus not represent/support any query activity being performed on a given read-only replica, and so could not support automatic tuning for any read-only replicas.

Is this correct? I’m hoping someone can disprove this, or provide some kind of work around. We’re getting serious query sniffing problems on some important read-only replica queries, and if automatic tuning will make this go away, management might buy into an upgrade.

(I was not able to find anything on this on the web, and hardly anything on automatic tuning.)