A very thin speaker wire might indeed demonstrate an audible "difference", but if so, it'd be a bad one. As discussed some time ago, it wouldn't necessarily involve a roll-off in the highs. There are two effects when a very thin speaker wire is used; the more obvious is that its higher resistance leads to more of the power being used in the connecting wire rather than being delivered to the speaker. This is because two resistances in series(e.g., the connecting wire and the wire in the speaker driver)form a "voltage divider", and the voltage leaving the receiver is used up in proportion to the speaker wire resistance as compared to the driver wire resistance, i.e, if the speaker wire was so thin and long that its resistance(e.g., 4 ohms)actually equalled the impedance of the speaker at a particular frequency, half the voltage(and resulting power)would be lost on the way to the speaker. Usually it's much less than this, of course, and typical receivers have plenty of power to spare, so this is the less significant effect.
The other, more significant effect is that since the speaker impedance usually varies widely at different frequencies, while the resistance of the speaker wire stays the same, the proportion of the total voltage and power used by the speaker driver likewise varies with frequency. This results in the frequency response fluctuating up and down with impedance and less accurate sound.
This is all a result of the well-understood voltage divider effect and no amount of reliance on a simplistic "Just trust your ears" mantra can change the facts.
