Does Change Data Capture (CDC) work in a SQL Server 2012 AlwaysOn Failover Cluster Instances setup?
Refer to Replication, Change Tracking, Change Data Capture, and AlwaysOn Availability Groups (SQL Server)
From the reference :

Change Data Capture:
Databases enabled for change data capture (CDC) are able to leverage AlwaysOn Availability Groups in order to insure not only that the database remains available in the event of failure, but that changes to the database tables continue to be monitored and deposited in the CDC change tables.
The order in which CDC and AlwaysOn Availability Groups are configured is not important. CDC enabled databases can be added to AlwaysOn Availability Groups, and databases that are members of an AlwaysOn availability group can be enabled for CDC. In both cases, however, CDC configuration is always performed on the current or intended primary replica.
Harvesting Changes for Change Data Capture Without Replication
If CDC is enabled for a database, but replication is not, the capture process used to harvest changes from the log and deposit them in CDC change tables runs at the CDC host as its own SQL Agent job.
In order to resume the harvesting of changes after failover, the stored procedure sp_cdc_add_job must be run at the new primary to create the local capture job.