The short answer is indeed no. I did some checking on this and found that on some systems so long as you don't hang up on the "session" you can type in some numbers and retrieve the deleted message(s). However, once you end the session (hang up) that kills any hope of a retrival process. It would be an ideal feature to be able to retrieve deleted messages say within 24 hours of deletion. This would require a lot of backup server space and a good deal of complication on Verizon's part. I think they would argue that it's just not cost effective for all the messages that are left daily. Still it might be a great idea as an extra paid service for that capability for those smaller numbers who are willing to pay for that ability.
I read a very tragic story on another site where a lady got a wonderful voice mail from her son in Iraq. She accidentally deleted it and didn't realize it until she hung up. She thought she hit the number to save it. I hate to say it but her story ended with him being killed and that was the last time she ever heard his voice. She was heart broken and begged the carrier to please retrieve it . . . but it was too late. I think she would have paid any amount to have that recording.
Are you listening Verizon? If so, take a good look at this as a paid feature in the future.