
Yes it is linked, he will be feeling hungry as he is on a diet and looking for other sources of food, unpalateable as the thought it, faces haqve still a lot of nutritional valuye, so many dogs on restricted food intake will indulge in this.
The only thing you can do is ensure that his toilet is cleared up right away.
As for assuaging the dogs hunger pangs you can give him vegetables like runner beans, unwsweethehd tinned pumpkin (popular in the USA) Carrots, and Cabbage to bulk out his meals. It will give more voluminous stools, but should help with the problem.