It does not make sense to me for you to add a local user to an instance of SQL Server on a cluster. You really need to consider that the resources etc that are required should be resources that will be available when one of the servers in the cluster has failed.

Hence, if your cluster consists of serverA and serverB and you create a user on serverA. What do you expect to be able to do when the active node is serverB and serverA is down ? You certainly cannot expect to be able to logon with that user because you cannot validate the credentials of the user.