The OED defines it as:
c. colloq. (orig. U.S.). to go for it: to put all one's efforts into achieving a specified end; to try one's hardest, to do one's utmost; to make an attempt. Frequently imperative in go for it!, used as an exhortation or to express encouragement or support.
It is defined as a colloquial phrase, but depending on your voice in your essay, I could see it working. That being said, if you tend to have a very formal voice in whatever piece you're writing, I'd suggest against "go for it."
However, I'm not sure if your usage is correct.
with 17,735 students went for it.
This doesn't really make sense. In fact, I'm not sure what "went for it" is doing in this sentence at all, as things look and feel just fine without it:
The second position belonged to part-time work, with 17,735 students.
As such, I'd play it safe and leave "went for it" off entirely.