Yes you should. Baby chicks eat around the clock to support the huge amount of growing they are doing. You should never let the food or water run out. They need both in large amounts.
Yes keep food and water available all the time. I have a round feeder and a long feeder in my brooder and 2 quarts of water. I have 30 chicks in the brooder and they are about 3 weeks old. They are eating most of the feed and most of the water every 24 hours. I am going to move them to the chicken coop and run probably this weekend the cold weather is basically gone here and the lows at night won't be going below 40's at night anymore. In the run I have a 5 gallon watterer and several feeders for them to use. They will be fine there It's predator proof and a nice yard for them to use they will enjoy it there with about a 20'x 30' place and out of the brooder.