[IIAOPSW]

No. Having the other 20 in-between values doesn't help improve the "accuracy" of the 2 khz wave. An x Khz wave is always an x Khz wave. That is to say the x Khz part of the signal is by definition the part of the signal which looks like sin([freq][time]2pi). Your soundwave is a sum of these Eg

a_i sin(2pitf)

where each a_i is the amount of a given frequency present. If every wave sample you have goes [1,-1,1,-1,1,-1...] then 100% of your wave is accounted for as a sin wave at the sampling rate. There is zero additional frequencies present with unknown amounts. If your wave samples went like [0,1,0,-1,0,1,0,-1...] the only frequency of sound present in the signal is the one at half the sampling rate. The whole wave is accounted for.

On a more physical level, its ok if your sample only sees +1/-1 every other sample, because when that electrical signal turns into pushing a magnet the magnet has to accelerate smoothly in accordance to Newtons laws. In other words, flipping the voltage between +-1 as a 40khz square wave becomes a perfect 20khz sine wave when it reaches the speaker.