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?

No, it wont as documented in BOL(for azure but still applies to sql server on prem):

Attempting to enable Automatic tuning via T-SQL on the read-only secondary will result in a failure as having a different tuning configuration on the read-only secondary is unsupported.


Is this correct?

Yes, it is. Erin from SQLSkills has a nice FAQ that says : Because the replica is read-only, and Query Store inherently writes data TO the database, you cannot enable it to capture queries that are executed against that read-only copy.
if you are running into parameter sniffing issues, you can use query hints (with proper testing) as explained by Paul White in his blog post