Possibly but not common

Maybe if you catch the old female. I haven't seen it with coyotes, but twice with wolves I've caught the alpha female and had the others howling all around while I dispatched and remade the set. I was also Guiding elk hunters a few years ago and could hear wolves howling all morning on the hill across the canyon. Turned out a trapper had a wolf in a trap over there that morning and the others were around howling. If that happens remake the set and slap in a couple blind sets quick if you have the traps, and get out of there. The others will be back looking for her.

On a rare occasion coyotes will kill a coyote in a trap. I've never been around when that happened, but I suspect there is a ruckus that you would hear if you were in hearing.