Why would ethanol not affect a chromate-dichromate equilibrium? Is it because it wouldn't readily give up an OH- or H+ ion that might alter the chromate-dichromate equilibrium?

The equation for the mixture is:

2CrO_4 \ ^- + 2H^+\rightleftharpoons Cr_2O_7 \ ^{2-} + H_2O

The dissociation of ethanol in water is:

C_2H_5OH \rightleftharpoons C_2H_5O^- + H^+

Ethanol hardly dissociates to give H+ ions (not OH- ions!! ). Hence, you can say no H+ is present at all (in fact, 1 out of about 10^16 molecules of ethanol gives an H+ ion). So, no H+ ion is added and the equilibrium is not disturbed.