Always-On secondary Replica's Read Committed Snapshot Isolation
Yes, when failover occurs the secondary changes back to read committed if that's how the DB is configured on the primary.  
The developers are the only ones that can tell you if your application supports RCSI.  It probably does, but if they designed it such that it depends on blocking to ensure things are done in the correct order, then it doesn't.  Many third-party applications do not document whether it is supported when it really is, so step one is to contact the vendor support and ask and go from there.