No, you cannot create triggers on system tables.
However, you can create a server-level DDL trigger for the task. Here is a quick demo:
CREATE TRIGGER modify_login_tri ON ALL SERVER
FOR CREATE_LOGIN, ALTER_LOGIN, DROP_LOGIN AS
SELECT eventdata()
go
CREATE LOGIN testing WITH PASSWORD = 'NotSoSecret'
ALTER LOGIN testing WITH PASSWORD = 'EvenLessSecret'
DROP LOGIN testing
go
DROP TRIGGER modify_login_tri ON ALL SERVER
The eventdata function gives you details about the command that fired the trigger.