Mark Bittman believes not

The argument for limiting the use of food stamps to actual food is consistent with established policy. They’re already disallowed for tobacco, alcohol, vitamins, pet foods, household supplies and (with some exceptions) food meant to be eaten on premises. Payments have been based on the cost of a "nutritionally adequate diet." Let me state the obvious: there is no nutritional need for foods with added sugar.

Jacob Sullum cries nannyism:

Notice that [Bittman] asks whether such meddling is "necessary," not whether it is legitimate, and even then does not answer the question. Instead Bittman suggests that people are addicted to sugar, which he thinks means they have no choice but to consume it and therefore must be rescued from this self-destructive habit by benign overseers like him. That is how he imagines the government is "on our side" when it uses force to stop us from eating what we want to eat. 

Earlier discussion of whether to regulate sugar intake here and here.