“My motivations were being a true believer in the possibility that a product like this could change the way we think about food,” she said, “and hold hope for the ideas we have about sustainability and environmental impact and other things I feel strongly about.”

Arizona’s best-known products are made from high-fructose corn syrup diluted with water or tea. Every eight ounces of Mucho Mango or Grapeade contains 110 calories, 10 more than in the same amount of Coca-Cola. Each 23-ounce can of those flavors, which Mission Chinese Food now stocks in a help-yourself refrigerator just inside the front door in Bushwick (under a neon sign that says, Great Buy!), contains about 70 grams of sugar. Rates of obesity and diabetes among adults have been slightly higher in Bushwick than citywide, according to a 2018 report by the New York Department of Health and Mental Hygiene.

In a telephone interview, Mr. Bowien said he saw the promotion — and others he plans with Arizona — “as an opportunity to reach more people.” He added, “We already appeal to people in the food world, but I really wanted to reach, like, kids that are familiar with Arizona to branch out and try something different.”

Mr. Bowien said he was not aware that the neighborhood had elevated levels of obesity and diabetes. “I don’t really have a comment,” he said.

Mr. Bowien’s Arizona-friendly menu items are not as sweet as they might have been, all things considered, although the cocktail is highly reminiscent of the sugary, chemically enhanced, watered-down margaritas served at the kind of Mexican restaurants where the servers wear sombreros and shot-glass bandoleers. The Green Tea noodles with ground chicken do, in fact, taste like green tea, perhaps because they are freely sprinkled with matcha.

If the grated mango and the mango jerky were both subtracted from the Mucho Mango fried rice, would any mango flavor remain? Maybe not.

Early one recent evening, the restaurant was giving away cross-branded cocktail cups and chopsticks to anyone who bought one of the Arizona items. The swag didn’t seem to be helping sales of the sponsored menu to the point of eclipsing more celebrated Bowien dishes like Chongqing wings or kung pao pastrami.