May 22, 2010 two pizzas (A value of about $40) were exchanged for 10,000 BTC.

At that exchange rate, $1000 of BTC would be 250,000 BTC.
At that time, there were about 2,852,150 BTC in existence.

So, acquiring 250,000 BTC would mean acquiring about 8.8% of all existing bitcoins.

Could it be done?  I didn't know about Bitcoin yet in 2010, so someone else would probably be better able to answer. My guess is: Maybe. Probably not all in a single purchase though. You'd probably have to complete transactions with many individual. But to create such a large sudden demand would probably have driven the price up pretty quickly. In the end you'd probably have ended up with a lot less than 250,000 BTC as each individual purchase would significantly reduce the pool of bitcoins available for purchase and result in a higher price for the next purchase.