20 liters of beer at an "average" carbonation level holds 50 liters (@STP) of dissolved CO2. While some of that was already in the beer from fermentation, the rest has to come from the gas bottle.
And in a typical Cornelius keg, there's only a liter or less of head space to fill with gas (albeit at higher than 1 ATM), so if you don't leave the gas connected that beer will never carb up to a servable level.
fwiw, carbing at serving temperature and constant CO2 pressure to achieve a typical 2.5 volume carbonation level takes me two weeks to be "ready" and another week to be "perfect". There are ways to speed that up considerably, but that ain't my thang