Small nit to pick 🙂

6.022 x 10^23 molecules = 1 mole.

1 cc = approx 1 gram of water.

Water is approximately 18 grams per mole.

Therefore, 1cc =~ 1/18 mole or 3.34×10^22 molecules.

Rest of your point stands … though even though there are a lot of molecules available in 1cc of blood, the tests for them have to actually be accurate. The accuracy, not the availablilty of molecules to test seems to be at issue here.