Yes, it works. It is a mild citric acid, which works to remove the corrosion and grime. Mix two or three packets in a gallon of water (no sugar added of course). White vinegar also works well.
If you want a nice shine after cleaning, get some 0000 steel wool from a hardware store or Walmart. It will polish the brass and steel parts without leaving any scratches. Finish with some metal polish to protect from future rusting.