If Vegeta killed Gero then no the androids wouldn't come to life (unless someone else did it). Future Cell would still come to the present universe we are watching, but since there are no androids he cant be completed and would get beaten. Then there's the larva cell being developed at the same time which will eventually be born.
However, if Vegeta didn't let Dr. Gero slip away they would never have found his hidden lab (It was Bulma who found out that android #20 was Dr. Gero, and knew his lab was some hidden cave somewhere outside of north city), I am sure Cell would have found Dr. Gero hidden lab since he was born there and because future trunks had no knowledge of Cell when he returned, and that will allow cell time to become Perfect by absorbing 17 & 18. I am sure cell has knowledge on how to activate 17 & 18 because he's not stupid. Thus becoming perfect cell and not giving the Z fighters a chance to get to know the enemy first. In a way, Vegeta's pride and arrogance kind of helped reveal a bigger threat in time for them to use the hyperbolic time chamber. The only other possible argument towards my statement is that given Cell attacked Gingertown and other cities as well he might have not return to the lab, but I think not because he returned to the past with Trunks' time machine to find android 17 & 18, one would think his creator's lab to be one of the first place he checks but seeing how Trunks blew it up I am sure he'll just keep on looking.
Hmm good point, I forgot that they only found Gero's lab because Gero led them to it, and Cell would have been born anyway. So even if they killed Gero, Cell would have eventually found his way because, as you said, he was likely programmed to know the location of 17 & 18. So Vegeta's arrogance isn't entirely to blame. But he still fucked up with the 2nd stage of Cell when he allowed him to reach perfect form. haha.
Well yes Vegeta did fuck up fighting stage 2 Cell; however, if Vegeta did not allow cell to become perfect and start the cell games Gohan wouldn't be able to become SS2, because there is no reason for him to be angry. Lastly, Goku wouldn't have sacrificed himself from the self-destructing Cell and return to the other world and learn to achieve SSJ 3 or how to perform Fusion. In a way, every time Vegeta messed up and let his arrogance get the best of him, it was best for the DBZ universe. The worse mistake I see Vegeta doing is allow himself get taken over by Babidi and turning into Majin Vegeta because Babidi was using the energy of Majin Vegeta and Goku fight to revive Majin Buu. Then again, it wasn't until shortly after he allowed himself to be taken over by babidi and becoming Majin Vegeta that he learn to become a better father, husband, and friend (hence, he blew himself up to stop Majin Buu).
I do have a question for you fellow DBZ fans. How is that both Vegito (Potara earrings fusion of Vegeta and Goku), Super Gogeta (Fusion dance of Goku and Vegeta), and Super Saiyan 4 Gogeta (Fusion dance of SS4 Goku and SS4 Vegeta) all have different personalities yet they are both a fusion of Goku and vegeta and their personalities.
I would imagine they have different personalities because they're all entirely different beings, not to mention the way they fuse together is different as well. I concede that Vegito is by far the best though.
Vegito and Gogeta have different personalities due to the differences in thier fusions. The only reason that the two forms of Gogeta have different personalities is that the base characters that create Gogeta had changed, as well, though less noticeably. After all minor changes in two personalities over time will cause a much more noticeable change when they are fused into a single personality (in my humble opinion).
It seems like Vegeta became a chef in Otherworld. Who knew 
Does anybody know why they didn't wish back android 16 after they defeated cell?
So I'm watching the episode of DBZ today where future Trunks travels to the past - or current, if you will - to warn Goku of the impending doom that is the Androids. While listening to Vegeta criticize Goku for his lame Yardrat gear, it occurs to me: Vegeta is responsible not only for the Androids but for Final Cell and ultimately the Death of Goku. Think about it, when Vegeta finally acheived his Super Saiyan form he could have easily blasted Gero to bits, but he was careless and ended up giving him enough energy to escape and unleash 17 & 18. In the case of Cell, Vegeta was easily strong enough to destroy him in his 2nd form, but instead he lets him live long enough to transform and fuck shit up. Anyone agree that if vegeta would have killed Gero the Androids wouldn't have been unleashed, or would they have been unleashed anyway? and what of Cell? Thoughts?
(P.S. - Vegeta is still a bad ass character, just exposing his flaws.)