Your hands will be at least a little damp and soapy. How did that happen, if latex is waterproof? It's because your hand doesn't make a perfect seal with the glove.
Also, dish soap and other detergents are surfactants, which reduce the surface tension of water. That makes it easier for it to get into tight spaces, like the space between the glove's edge and your hand.
Finally, latex is soluble in many kinds of oil/petroleum-containing product (many waxes, some heavy-duty cleaners, etc.), so if you're wearing latex gloves, you'll literally be dissolving latex onto your skin and degrading the gloves. Gross.
If that's what a three-second test will do, imagine how it'd feel to wash clothes for thirty minutes. Not pleasant.