I don't usually have a problem, its sent at the same time, I think you will find that the voice turnout is not related to the MDT/Pager message, it all depends when the operator hits send. If the operator starts the broadcast before hitting send then you will get a delay.
I have the SAMFS dispatch channel on my scanner on VHF and all I usually get for calls we are responding to is the tones and the "Attention , Attention" and the pager goes, so its not really any advantage. Its gives you a minor heads up, eg: you might get the brain thinking fire call, before the pager goes.