Can a cat tell when a human is sick?

No. If a cat meows a lot, it either wants something from you (food, a door opened, to be petted) or it just likes talking (certain breeds are known for this.) Some cats will meow more than others.

If a cat is in pain, they may cry out, especially if you try to touch the effected area. But this kind of shriek is very obviously a cry of pain, and is different than a normal meow. Sadly, if a cat is sick, it is very hard to tell; like most predators, cats attempt to hide anything that is wrong with them, so they won't be seen as weak. If a cat is sick the signs are usually very subtle: decreased appetite, low energy, glazed eyes, etc.hhh