Berkley,
Unfortunately the answer to that is no with the embedded voice processor.
You can do a Forward Only to the message and it will be deleted immediately, but you are also hoping they never have issues with their network or email service. I am not sure if the Deleted Message Hold Duration would provide a reprieve of up to 24 hours on this or not as I have never tried it.
If Enhanced Integration is a viable option then when they delete it from their email it is deleted from voicemail. There is a timer that allows the system to hold the deleted message for up to 24 hours, but it is set to 1 hour by default [Deleted Message Hold Duration].
Sorry,
TE