
I can't say whether this particular test is genuine or a rip off, but it should be possible to test for cocker coat genetics as they are known..
Red requires a pup to receive two red genes (ee) - red is recessive so a dog needs to have two or it won't be visible. Gold requires the two recessive red genes AND two liver genes (bb) which are also recessive.
Recessive genes can hide and be passed on for generations because you need two copies for it to show, so even if she does get her dog tested she obviously needs to maximise her chances of it appearing in pups by picking a stud dog who red or gold.
I must say - big disclaimer - not a cocker person, mainly my colour genetics knowledge comes from snakes! (Where things are on the whole, a lot simpler as most colour genes are recessive!)