No, probably not!
The probability that coprophagy (that’s the scientific name for this problem) begins in the litter box and the direct environment in which the dog as a puppy was born, is very big.
For dogs living more or less in a pack, the mutual pack relationships also plays a part, and for eating faeces there are, next to the known causes, factors such as order of rank and dominance that play a part. It is a kind of substitute pattern for defending their part of the prey.
In Canada, I once observed that sledge dogs weren’t interested in eating their faeces as long as they were all connected to their chain or doghouse, so as long as everyone had its specific place. But when for one reason or another one dog would break loose, the other dogs would defend their faeces or gobble it up as if it were a meal whenever the free dog would come near them.
This territorial behaviour and possessive urge are considerable factors here. It is almost always about letting off steam, or about substitute behaviour, and the better they feel, the more steam must be let off.