I am going to throw in a personal note here: I find these kinds of questions speculating on how to kill human beings more effectively extremely distasteful. This is not a video game, we are talking about millions of innocent men, women and children, including tiny babies, who were really killed, in real life, within living memory.

To answer your question: no, it is not easier or faster to force people to drink poison. You would have to stand over each individual person and force the liquid down their throat. People would choke and sputter and throw up. What if they refuse? You'd have to shoot them, which is exactly the kind of laborious procedure the gas chambers were designed to do away with. Initially, the victims were shot out in the open by special forces, but this proved too slow and above all too taxing for the perpetrators.

It is faster to herd people into gas chambers where they will be killed by the thousands in twenty minutes. Because they were packed so tightly a relatively small amount of gas was needed. There were ventilation systems in Auschwitz. The hauling out was not done by Germans but by prisoners. The Germans were never in danger.