Pumping!

I exclusivly pumped for the first 3 months with my first baby and plan to pump for this one as well. My breast are already leaky but im not due for another 10 or so weeks. Can i start saving what im letting down? And is it okay to pump befor baby arrives? Say around 35+ weeks? I just want to save what i can and keep stocked as I had issues keeping a supply after 6 months with my 1st.