I don't think they will. Or rather they won't deliver anything as good as what they promise. Imagine you're testing for something that requires 10 modified white blood cells per million. A pinprick drop of blood has about 7,000,000 white blood cells in it. So you might expect to see 70 modified cells... but only if those cells are evenly distributed throughout the patients blood. They're not. They're randomly distributed. So the statistical likelihood of getting a false negative is high.

The answer to that is to take more blood, from a vein. You can't make a more accurate test because you simply don't have the necessary information. If you do take more blood then the test gets as expensive as a normal test and you no longer have any cost advantage.