I have hunted plenty of times without a lead in bulldog as a catch dog. But when I have hunted with straight curs, there has always been a catch dog in the bunch, the catch dog just happened to be a cur. Biggest hog I have ever caught was shut down/ caught with 3 cur dogs, not a bulldog in sight.
Any time I hunt horseback, I only run curs. My bulldogs don't have the leg/lungs to hang with the horses, and there is not enough room in the saddle for my big butt and a bulldog