I have shot pigs on several occasions and then waiting, hoping more pigs would show up only to have deer show up. A gun shot won't scare away the deer for very long, assuming any are actually close by. More than likely the deer will not stay around a long as the hog is around, however, and the hog will likely eat much of your bait in the process.
I shot a Sow Saturday evening pretty late. Figured it likely ruined my deer hunting for the remaining 30 minutes of light. Waited until dark to drag the pig out. Checked game camera the next day and much to my surprise there was a buck under the feeder exactly 12 minutes after I left....dragging the pig behind my vehicle.
I saved both videos (me leaving with hog and buck feeding 12 minutes later), so yes...sometimes it doesn't bother them. Of course... it was after hours (dark) when this happened.