Does not sending SAT Essay scores to "SAT Essay Optional" schools worsen your chance?

HYPMS as well as other schools that I will be applying to do not require the SAT Essay score. However, “not required” can sometimes mean “recommended”. One reason that these schools made this choice is to help low income kids out and I am indeed a low income kid, like I get free lunch at school. Is it OK if I take the SAT without the essay?

In this case, unlike Subject Tests, I am of the opinion that “not required” does not mean “but we still expect them.” Not doing the SAT (or ACT) with essay is fine.