You need to think of Always On in terms of Log Shipping or Mirroring. The secondary databases can be configured to read from, but you can't update them directly, so you can't apply an alternate set of indexes. To do this you would need to use replication.

With replication you can replicate only the data (and the required Primary Key), and then configure alternate indexes on the subscriber database. This can be very effective, allowing you to exclude data you won't be reporting on since replication can be configured at fairly low level.

Cheers

Leo