With a v60 (and many other types of filtering), the filter itself doesn't do the majority of the filtration. The bed of coffee grounds basically act as a filter for themselves (obviously held up by the filter papers at the bottom). It's why if you pour aggressively or stir the grounds as it's filtering, it will draw down way slower; fine grounds that would otherwise be trapped by courser grounds end up lodging themselves in the pores of the filter paper.

I've done the same process you are suggesting (and the same process but for filtering milk punch), and it was slower than filtering with everything. I think technically, the fastest might be decanting the supernatant into a separate container, spooning the grounds into a v60, and then pouring the supernatant through it gently.