Not necessarily - it depends on how long you're storing the F&V, and what your preference is.

So, for a watermelon based juice served on a hot summer's day, you probably want everything to go in chilled so you can serve it straight away.

But for your regular veggie/fruit mix, I don't think it matters too much. Do, however, make sure you have washed everything thoroughly unless you're going to peel it.
I am not also used to refrigerate F&V before juicing, from what I know after you have juiced you can store it inside the ref. If you happen to cut and peel F&V you can only keep it inside the ref for around 2hrs before juicing