No, it will not. Veeps don't sign or veto bills.
Balancing the ticket is a time-honored practice throughout the political world, and is particularly noticeable in presidential elections. It has been used in successful
campaigns (for example, Kennedy-Johnson in '60), and in unsuccessful campaigns (Kerry-Edwards in '04).
If Giuliani wins the Republican nomination, it seems a good bet that he will choose a pro-life, pro-gun VP candidate to run with him - for the express purpose of inspiring conservatives who otherwise would not consider Giuliani to come out and support the ticket.
Will it work? I think it will.