Our setup already has two sql servers running in failover cluster for SQL AlwaysOn HighAvailability and a new office on the opposite coast setup to connect to primary office over site-to-site vpn. The plan is to move second server to secondary office and have it run in failover cluster from that location. I am concerned about how well the other office (one that is not hosting primary replica) will function since the software will be connecting to sql server on opposite coast. 

My question is how much delay is the office not hosting primary replica will see when reading data, and how much delay would office hosting primary replicate see when writing data.

If you want to move database to your new office use Geo-Cluster.

Your cluster disks data will replicate. The speed is really repends on how fast is your network and type of network used.

why don't you consider cloud.