I am having the exact opposite problem
When i remove the FQDN from the alias the service will not start and I get the below error messages: one in Windows application log and the other in the agentout log
SQLServerAgent could not be started (reason: Unable to connect to server 'MyServer\instance'; SQLServerAgent cannot start).
2017-07-21 08:54:04 - ! [298] SQLServer Error: 802, SSL Provider: The target principal name is incorrect. [SQLSTATE 08001]
Any help is appreciated
Jeff