I really don't know for sure. Maybe someone did a study on this, but I don't know of one. So I'm just going to give you an answer based on an anecdote.
There's a guy at my gym who does 50 pullups every day. He never trains them weighted. I challenged him in the early winter to a max weight chinup contest; he nearly beat me, and I was routinely doing weighted chinups, while he never did them. He developed good limit strength without using very heavy weights. Of course, he was doing pullups at ~50% 1RM. A good minimum deadlift is maybe 405, so a good working weight, taking my example into account, would be ~200lbs. You'll need a barbell & some weights eventually. A persons lower body is very strong, and DB's ain't going to cut it even medium term.
(Note: This isn't quite the same as what you're asking, since he wasn't doing them fatigued. I also don't really know what else he does for back work, but it doesn't seem like much at all. This also isn't doing lower body work; it's possible the upper body responds differently, and maybe even pullups specifically .. etc etc etc.)
Ideally, you should join a gym or acquire some cheap second hand equipment. We know you can get the benefits of heavy squats and deadlifts from actually doing heavy squats and deadlifts.