Well, sure but anything will be bad if used improperly. I've been in a minimum of one training class a week (either agility and/or obedience) every single week since about 3 weeks after I got Meg. That's three years. Am I "over-doing" it?
Some people who only see her in certain situations may think she's being 'over-trained', although I hope nobody ever looks at her and thinks she unexcited by life. I took her to the Little League field last night when there were a million kids/dogs/adults running around like lunatics, and trained a bit. Heeling, laying quietly, not getting up when people walked by, etc. I don't want her getting up and trying to visit every human who walks by, so I'm training her not to. But it's a behavior she's learning to perform, not an attitude adjustment I'm trying to create.
So I guess what I'm saying is - if you are thinking about a particular dog you know, how often do you see the dog and in how many different situations? If you are asking in general, I absolutely think that some types of training can create a shut-down, unhappy dog very easily. I also think there are some amazingly well-trained dogs who adore their lives and their work, and who may never go great people or other dogs because it's been trained into them. They are often the same dogs who I see doing all their obedience "in drive", like the enthusiasm Lyric clearly showed in his training. Prompt obedience and good behavior don't have to mean shut-down and unhappy.