Sql-server – Does Change Data Capture (CDC) work in a SQL Server 2012 AlwaysOn Failover Cluster Instances setup

No. During a failover, clients will notice. Your connection to the SQL Server will be broken, and you'll have to retry your transaction.

Yes AG support multiple subnets as described here. Also make sure that your data provider supports MultiSubnetFailover .. .NET Framework 4 supports it.

To answer your question ...

IF you use .NET framework 4 or 3.5 then the provider will support it as described here.

Also, a good reference to SQL Server Multi-Subnet Clustering is well documented.

With legacy client libraries or third party data providers, you cannot use the MultiSubnetFailover parameter in your connection string. To help ensure that your client application works optimally with multi-subnet FCI in SQL Server 2012, try to adjust the connection timeout in the client connection string by 21 seconds for each additional IP address. This ensures that the client’s reconnection attempt does not timeout before it is able to cycle through all IP addresses in your multi-subnet FCI.