He'd just end up draining all his Ki before he could kill Boo and just dies again. This changes the battle against Pure Boo a lot though, since a dead SS3 Vegeta would be able to kill Boo as soon as Galu wastes his Ki. Therefore, there's no return of Good Boo or Vegeta acknowledging Goku's superiority, nor will Oob exist unless Enma makes the decision himself so as to not deal with the possibility of Boo wrecking his office.
As for Super, I doubt this would change the plot so much. Whilst Beerus probably wouldn't try to destroy Earth if he got his pudding, Goku would probably still confront him not long after the party with the idea of using the Dragon Balls to learn about the SSG. After that, the plot continues as normal seeing as how Boo plays no significant role in later events. I doubt Vegeta not getting his rage boost would affect his progression much, considering he could just do the God ritual himself and training gains are plot related anyway considering how strong most of the supporting cast got (Piccolo, Kuririn, Gohan, #17, etc.)