Peyton Manning will not veto the pick, well, because he is not the general manager.
Manning, however, will certainly make this an interesting situation should the Colts be granted with the first pick in the draft.
Manning is most beloved athlete in Colts history, and he will hold a lot of PR leverage. If the Colts pick Luck and he is everything they hoped he would be, the Colts may be forced to trade Manning, which will cause a Steve Young/Joe Montana situation.
Manning is more than just a quarterback to that team; he is the face of the NFL and an icon in the city of Indianapolis.
If the Colts are given the right to choose Luck, Manning will argue that the Colts can use the pick to trade with another team for a boatload of picks. Assuming that Bill Polian actually drafts well with them (which is something he has not done in some time), the Colts can come back next season fully reloaded with a healthy Peyton Manning in another quest for a title.
Manning is not going to "veto" the pick, but his opinion certainly has some weight in making that decision. I still believe that the Colts will pick Luck, however, just because an opportunity to have two of the best draft prospects at the position fall in you lap twice in a row has never happened.
It may be an ugly divorce from Manning, but it could lead to long-term prosperity for the Colts.