^
Of course it doesn't affect the gearing ratio; that's a function of wheel size, cog size, chain ring size, and internal gearing (if any). But if crank arm length affects how power is delivered, it likewise affect how much power is, or can be, delivered; and of course it has biomechanical implications on wear-and-tear on the knees &c. But we quibble.

By the way, if you want to give short crank arms a fair trial, a three speed is not the best way to do it. Short crank arms work much better if you have a lot of gears to chose from, so you can maintain your 90 rpm cadence at almost any speed.