The Non-Executive Branch VP

Over the last two days I've been reading a lot on the Constitutional theory being expounded by VP Chaney's office that the office of of the Vice Precedent (OVP) is not a part of the executive branch.

"The Vice Presidency is a unique office that is neither a part of the executive branch nor a part of the legislative branch, but is attached by the Constitution to the latter. The Vice Presidency performs functions in both the legislative branch (see article I, section 3 of the Constitution) and in the executive branch (see article II, and amendments XII and XXV, of the Constitution, and section 106 of title 3 of the United States Code)."

I'm not going to contest this theory here, rather I'm going to explore some consequences that follow from this position.

First, if the OVP is not a part of the executive branch is not the OVP out of the chain of command? If the VP gave an order, directive, etc to a member of the executive branch would not that order, directive, etc be unlawful? This would be of particular importance the military.

Next, can a person or office hold a position of trust in the government of the United States and not be a member of the executive, legislative, or judicial branches? Related to this is can the President delegate any of the duties, responsibilities, or authorities of the Executive Branch to someone who is not a member of the executive branch? Could this be done for the Office of the President of the Senate?

Does the OVP have 'executive privilege'? Or for that matter any of the rights, privileges, or prerogatives of the Presidency and/or can the Precedent extend them to the OVP?

Finally how does the Congress fund the OVP? Would not the Congress have to fund the OVP separately from all the other branch's of government? If fact could they do this legally or would they need to fund just the Office of the President of the Senate?

It seems to me that this argument makes the VP just an office that has no right or ability to participate in the government of the United States. That all authority for the VP to do anything derives from his position as the President of the Senate.

What's your take?