Not sure what pathogens you are talking about. Once hogs have been on pasture, there is going to be some amount of damage from rooting. Unless the hogs are ringed and run through there fairly fast, the pasture is really going to need some work. Tilling or at least dragging. Holes should have to be fixed. If the hogs do much rooting, the pasture will be less usable.
Lepto is the biggest problem with feral hogs. "They say" that it is not transferable between species. But is a fact that since feral hogs have gotten to be so bad in Texas and other states, the incidence of lepto in cattle has skyrocketed. Lepto causes abortion, breeding problems, cattle just not "doing good".
Please elaborate on what pathogens you are referencing.