No - to be elected Veep, one must be eligible to be elected POTUS.
Why all this talk about Bubba as the VP? We're talking about the torch and a senator slot from NJ.
There is some arguement EXACTLY what the Constitution means on that point.
Technically, Beelz-a Bubba would be able to serve 2 years of a unexpired term since he is allotted a maximum of 10.