Edition upgrade on SQL Server failover clustered instance
No, unlike Service Packs and Cumulative Updates where you're responsible to keep the bits in the same state across all nodes, the Edition upgrade applies to both nodes at once. I applied it myself to the 'passive' node and Configuration Manager on the active node showed Enterprise immediately. You still need to restart the service though, as SSMS showed Standard in Properties even after refreshing and reconnecting, but immediately reflected Enterprise after refresh once I'd restarted the service.