Well... honestly, no, that's not science. If you look at attempts to formalize the scientific method, you probably won't see a step that is, "convince other people", and there's a reason for that. The process of convincing other people is political, and not really a scientific process.
Yes, that part of science is political but it is still part of the scientific process. You can't separate science from humanity, thus it is a CULTURE. That culture has many aspects, like the process you speak of, but part of it is convincing others that one theory is better than another. It effects, not only what is studied and funded, but what methods are favored and in the end taught.
There was a great CBC program on this recently, I can't link to it directly cause for some stupid reason the internet filter at work thinks CBC is a bad site to visit... But it's on CBC Radio One, Ideas and called Knowledge and Democracy. A sociologist of science explains this very well.
"Well, it don't make the sun shine, but at least it don't deepen the shit." -- Straiter Empy, in _Riddley_Walker_ by Russell Hoban