Yes, but the average value of the sampled values will tend towards a Normal distribution by the central limit theorem, and I'm probably misapplying it by wondering whether the next sample tends to be from nearer the middle. I think skimbrel is right that as the sample being drawn from is decreasing each time the CLT will be invalidated anyway.
The average of the sampled values will be normally distributed, but the values themselves will be uniform.
If you sample every number once from [0,100], the average is 50, but that doesn't imply that the distribution of the sampled elements is normal - it's uniform.
His question of whether "on average, does the next card come from the middle" (which it doesn't) isn't the same as "is the mean of the next sampled card in the middle" (which it is).
The language was a little misleading - he said "on average" when he intended "most frequently".