All dns(Domain Name System) does is translate a letters web address to a number ip adress, doesn't have anything to do about the quality of your files at all. If it fails at its job, it won't be able to download the video at all.
Unless the file gets corrupted or IDM somehow captures the images of a stream in real time, downloading something won't affect the file in any way.
Many JAV video stutter because people capture them with software capture from streaming sites and that pretty much always mean dropped frames(which get repeated to fix it so looks like stutter on playback) in the video so it's probably a coincidence you only noticed the stuttering with google DNS.
