Well, for me, it was always a yes! With rules, but yes.
I taught Spark Plug when he was a puppy to wait until I said, "GIT IT!" for him to grab whatever tug toy I was dangling in his face, and then to "drop it" on command, and not resume until given permission to GIT IT again! Even novice handlers can play tug safely, and when played properly, tug-o-war has huge advantages.
1) You really can teach some patience, respect, manners and control of the mouth with these rules.
2) Tug is a GREAT energy-burner. It is interactive, fun, a huge tension release, and excellent exercise for your dog... and certainly for you, if your dog is a pit bull.
3) Tug can be great for building confidence in your dog.
Although, as previously stated, Spark learned to play tug with manners, we have vehemently played tug all his life. With our recent delve into training for Protection Sports, I am so glad this game wasn't something I discouraged. When he was younger (Spark will be four in August), you couldn't lift him off the floor by a tug toy for long, and you certainly couldn't swing him in circles by his toy, not that that was ever the goal, especially then.
I inadvertently "trained" him to hold on for longer by picking him up off the ground just a little bit, then quickly putting him back down, maybe even letting him win the toy, and praising him like he was the bravest dog in the world. Spark's reaction to that was to bounce off throwing his toy around, and then come back with it to resume the game: ideal.
Now, I am only five feet tall, and weigh accordingly... Spark Plug weighs 55 pounds on a good day. I am physically incapable (at this point...) of swinging him around too much. This is what I mean... I can't do this: