I was wondering if it would be possible to create a mod that allows you to drag the 1x1 Grass park tile, to make grass areas in parks, or to fill in gaps.
Yes, it would be possible, however it's probably something there isn't much of a demand for, and would also have to be part of a network, which causes more problems.
I think were actually talking about the draggable ped mall here, since there is the one plain grass variation ped mall piece that I use for wealthier areas when I want to match the area.