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.
Elijah. There's two separate questions here:
1. Is DTC supported with AlwaysOn Availability Groups?
You're using SQL Server 2012, and according to Microsoft's Documentation, that answer is no. I totally understand that you want to try it anyway, but keep in mind that you're now putting something into production that Microsoft simply will not support, AND you're using two separate niche features together (AGs and DTC). If anything whatsoever goes wrong, you're going to be in a world of hurt. This just isn't something I'd ever even think about trying in production.
Keep in mind that if your managers find out that you deployed something Microsoft specifically says in big letters, "YOU CAN'T DO THIS," and you have any kind of outage where you have to call Microsoft for support, you're going to have some ugly explaining to do.
Technically, DTC is supported starting with SQL Server 2016 SP2 and later, but it just means that you can pick which database loses data on failover, and the application has no idea data was permanently lost. That's not what a normal database administrator would call DTC support.
2. How should DTC be configured in a multi-node, multi-subnet cluster?
Read Allan Hirt's post on configuring DTC with multiple instances of SQL Server in a cluster, and make sure to read all of the links in the post as well.
Best Answer
Build a new cluster with an FCI and migrate the database using backup/restore. If you are not using VMs and need to reuse the existing server, then create a new 1-node cluster with an FCI, migrate the database, then rebuild the existing server, add it to the cluster and expand the FCI onto the second node.