1) If the "star" = performer gives his/her talents a little effort,i.e. he or she uses his/her talents wisely, s/he will become famous and a celebrity; or
2) If the performer is given a little chance, s/he will become famous and a celebrity; or
Given the context, I believe it would be the former (first).
[Edit: and after reading Gwen Stefani's lyrics, I believe even more that it is the former. She is saying in her song that she is wary of celebrity. All involved in it "party" hard and live a fast lifestyle, but in the end, they all are men and women with the same desires as the rest of us. ]
Hope this helps,
I’m the one they feed upon Give a bit a star is born
And if you're hot enough you'll get the pass
And you can tell your friends how you made it back