The short answer is no. Tap water in Cancun is not recommended for drinking, even for locals.
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Most private hotels and restaurants in Cancun will have an on-site filtration system installed or offer guests drinking water that has been purified or bottled.
Although there will be some bacteria in the water from the tap it is fine to brush your teeth with, even if you are at a place where you can't drink the tap water.
As a precaution you should not drink tap water in Mexico even if it's purified at the source. Most resorts and hotels provide bottled water or large jugs of purified water for you to refill your bottle. Velas Resorts stocks its suites with bottled water daily as included in it's all inclusive plan.
If you want to avoid traveler's diarrhea, there are some simple rules to follow. First, forgo tap water and opt for bottled water instead. It may not be the best for the environment, but it will be better for your gut. Second, make sure you eat foods at the temperature at which they are safest to be eaten.
While you should not drink the water in Cancun, the ice at hotels and restaurants here is usually filtered and purified so you can have ice in your margarita without getting sick.
The best time to visit Cancún is from December to April during the peak season. Even though the crowds are heavier, you'll experience near-perfect weather and find some of the cheapest flight and room rates for a winter getaway at the beach.
Fresh fruit with a thick skin you can peel yourself (such as bananas, oranges and mangos) is generally a safe bet at an all-inclusive. If you're concerned about water quality, you can always give fruit an extra wash with filtered or bottled water.