Can you paint a satellite dish? YES!
A lot of tailgaters bring either DirecTV or Dish Network dishes to the tailgate, and they are almost always the same dull gray that the factory puts on them.
In researching, people say that you shouldn't paint them, and to never use a gloss paint. When we started our tailgating, we used the factory dish. Not long after, we painted the dish with a flat red, and it worked fine.
When we had our tailgate truck painted, we opted to have the dish painted with the same paint as the truck; a dark red with a clear coat put over it. We then applied vinyl decals to it.
Did it still work? Sure did. No noticable loss in signal. So can you paint your dish and have it still work? Absolutely.
Even with the gloss paint, we've never had a problem with a reflection melting the LNBs like some say can happen.
So get out there an paint your dishes!
Picture from www.tailgatetruck.com