It sure can
The only time the program connects to the internet is when you first open it to see if there is a new version or not. After that it doesnt touch the internet. So you can safely run it while the internet is off
The reason I ask that you stop your AV protection is because a lot of AV's can get in the way of the repairs trying to run and can cause problems. Like in some they have sandbox modes and that would keep the repairs from working, not to mention it will slow the repairs down.
Sometimes the AV's dont get in the way sometimes they do. So it is better to keep them out of the way when the repairs are being done, but it is up to you
Shane