Should yogurt taste carbonated?
That's not a simple question to answer.
Some yogurt actually IS carbonated. Indeed, yogurt soda is common in mid-eastern cuisines.
A natural yogurt with live cultures will continue to ferment in the sealed package. The top seal will, indeed, expand. Some yogurts and similar fermented products (kefir; maslanka) have label statements advising of this. Kept long after its best before date, the fermentation gasses may actually force the seal open. You will likely have very strong, sour yogurt. It may not be to your taste, but it probably won't be spoiled.
In short, if the yogurt has live cultures, no mold, and smells/tastes okay, it's likely fine.
If it seems "off" to your nose or palate, I'd toss it.
But if your yogurt is a standard North American brand with dead cultures, and (especially) if it contains stabilizers, I wouldn't eat it.
I had this happen with a whole pack of organic yogurts when I was pregnant (therefore more cautious about what I was eating). It was also new packaging for that brand, so I emailed the company for a refund and to ask if it was dangerous. They did give me a refund, and agreed the yogurt shouldn't have been that way, but also assured me it would not have hurt me if I had eaten it.