In this case if more than one trigger property is specified they application will throw a IllegalStateException.  It will state in the exception that the bean has already been registered. 
For example:
Could not register object [org.springframework.scheduling.support.PeriodicTrigger@36341] under bean name 'trigger.newTrigger': there is already object [CronSequenceGenerator: */15 * * * * *] bound

I can put the original check back.