Does SQL Server route connections to a secondary replica which has commit mode as synchronous in case of an AG with multiple secondary nodes?
It will depend on your routing list.

SQL Server 2104 and SQL 2012 read-only routing directed traffic to the first available replica in the routing list, unless it was not accessible, and then it would direct the connection to the next replica in the routing list. When you have multiple secondary replicas available for read, it is not possible to spread the read load across those replicas.

In SQL Server 2016 you can configure load-balancing across a set of read-only replicas.

Details Here: https://blogs.msdn.microsoft.com/alwaysonpro/2016/05/02/sql-server-2016-alwayson-availability-group-enhancements-load-balance-read-only-routing/