Yes, you can use "fat" as a noun without an article. The word "fat" can be countable or uncountable, depending on the usage. In everyday speech, it's uncountable, and refers to body fat in animals, both the kind in our bodies and the kind in meat. Here's an example referring to food:
Most people eat too much fat.
And here's one referring to humans:
These biceps and triceps exercises will help you get rid of arm fat and tone sleek muscles.
In chemistry, "fat" is often countable, and refers to a type of molecule:
A fat (or oil) is formed when three fatty acid molecules react with a glycerol molecule to yield a triglyceride (and three water molecules).
Here's another countable example from a cooking site:
One of the most important things you'll want to consider when picking out a fat is smoke point.