Can a query whose execution plan uses parallelization use the cores of a processor on a another server that's part of the same Availability Group? If I have two servers (server A and server B) that are part of the same Availability Group failover cluster, and a query running on server A has an execution plan that uses parallelization, is it possible for that query to use cores from a processor on server B?
No, execution plan parallelization refers to using multiple cores on the server executing the query.  Parallelize plans are not executed across availability group replicas.