Yes, you should go early if the center at which you are taking FP is not very busy. It won't hurt to try.
I did the same thing. I had appointment for August 3rd. And I went on 26th of June, just a couple of days after I got FP notice. I told them that I will be out of station in august. As Seattle center (at burien office) was not crowded, they let me. Now my case status is "On 9th July we got the results of your FP & process has been resumed ...etc..etc".
So, basically, you will be helping yourself by making your process faster.
Hope that helps.
Mugdha.