The VP can never be PPT. BK was a Senator during his time as PPT.
The VP can run the Senate through his job as President of the Senate which happens everytime the Senate starts or when the PPT becomes prematurely vacant. It also can happen as part of a mutual power sharing agreement between the PPT and VP, something which I would very much desire, yet I have never been able to get the VP play ball. Atleast not recently. 
There are Atlasians amiable to that should they be brought to the VP position.
