The -pri argument tells the machine that created the key store to also export the private key to the xml file. Without it, you only export the public key. Your procedure for importing and authorizing users remain the same.

aspnet_regiis will allow you to import just the public key, but you would only be able to use it to encrypt sections (not decrypt). If you encrypted your connection strings on the first server and installed just the public key on all the others, only the first server would be able to connect to the DB. The rest wouldn’t be able to parse the config.