Yes. I'll spin it dry using my rotary to get as much water out of the pad as possible and then take a WW MF towel and work it dry even more. It is inevitable that it is still moist however i actually like that with some polishes.
I have never had any issues with using a still slightly moist pad. I will emphasize that i try to get it as dry as possible after washing it out.
I keep a few pads on rotation. After I spin them I sit them infront of a fan for a few mins. I learned the hard way when I started. I picked up a just cleaned and spun pad, the pad felt fine. About 30 seconds into polishing it shot out water/polish everywhere lol. Clean up was a biotchh