Dog hunting deer can be tremendously exciting. The first few deer I killed, I killed in frontof some great dogs in the swamps of LA. Unfortunately, dogs cannot read a posted sign. And yes, they play hell with stand hunting when they are not running. However, the way you describe it, I disagree.
Deer run by dogs do not leave the country. They only run far enouogh to avoid the dogs. Then, given a day or so, they often return to the area they were jumped in.
The problem is, they tend to avoid the permanent stands and seek new travel patterns. This means you had better be one heck of scouter with a climbing stand and know how to read sign.