If it originally came with one, yes...
They do a minimal job of keeping dirt out....note the use of the word minimal.
4000+ wheels built since 1984...
1. I do not claim to be an expert in bicycle mechanics despite my experience.
2. I like anyone will comment in other areas.
3. I do not own the preexisting concepts of DISH and ERD.
4. I will provide information as I always have to others that I believe will help them protect themselves from unscrupulous mechanics.
5. My all time favorite book is:
Kahane, Howard. Logic and Contemporary Rhetoric: The Use of Reason in Everyday Life
They're called hub dust caps, and not readily available except for the most expensive hubs. If your hub is fairly common a local shop or bike coop might be able to find a used one in the "junk hubs" bin.
If it's a freewheel hub, it's less critical since the bearing is recessed fairly deep behind the freewheel. If you don't have one for the right side, you can improvise one with a piece of thin metal or rigid plastic cut out and trapped between the freewheel and hub.
An ounce of diagnosis is worth a pound of cure.
“Never argue with an idiot. He will only bring you down to his level and beat you with experience.”, George Carlin
“One accurate measurement is worth a thousand expert opinions” - Adm Grace Murray Hopper - USN
WARNING, I'm from New York. Thin skinned people should maintain safe distance.