Yes, that would work! I use 5 gallon Tidy cat buckets with Rent-a-Coop watering cups. I drilled the appropriate size hole approx an inch from the bottom of the bucket and screwed the cups in. They work great!
However, if you live in a cold climate during winter months you will need to temporarily use a different waterer until the weather warms back up because the cups will freeze and not work.
I live in Michigan, our winters tend to be quite fridged. I use the cups during the summer/warmer months, so the chickens can dip their wattles to cool off and whatnot and I use the horizontal drinking nipples for winter. I then place a bird bathe water heater that's suitable for use inside the plastic Tidy Cats bucket to keep the water from freezing.