If you try waterproofing it it might afford some degree of protection from drips etc. Fill it with water first and get an idea of the base first. Mine leaked like a sieve on the bottom. It was breathable only because it was porous...like a sock.
Thing about tarps and bivvi bags is...I served 8 years in the Infantry in the days before this kinda thing was issued. We used 58 pattern ponchos as the tarp, set very low to the ground, and 58 pattern feather sleeping bags. We had no bivvy bags and roll mats were just coming around by the mid eighties. I don't ever remember getting my bag wet and that was with two people under one poncho with a second as a groundsheet.
I use an Army goretex bivvy bag now but I consider it a bit of a luxury. Don't get me wrong I like it. They can help by keeping wind chill off the sleeping bag and will keep the bag dry for sure but not strictly essential. If it's not raining I usually keep mine down at my feet and only pull it up if I'm feeling a bit cold in the early hours.
All that said the reason the old poncho worked as a basha is because we pitched them so low. The higher the tarp the more likely to get the bag wet. Now at 50 I don't want to be crawling into a tarp set 2 feet from the ground which is why I like a tarp big enough to have some height but still have the bottom edge low to the ground.