If the number is blocked on the phone, you can't stop them from leaving a voicemail. You could block them through your MyVerizon account online which will prevent the number from calling your number completely including voicemail.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
so that's the difference between blocking on phone or within myverizon, good tip!!
i have to agree, getting vm's from blocked callers is irritating but i need more than 5, so i block on the phone.