If air is leaking in while the system is cold, it will begin to condense and freeze on the walls of the chamber, until the walls become saturated, or the cooling power is no longer enough to cool the gas leaking in. At which point it will stay in the chamber as a gas, and act to conduct heat from the inner shields to the OVC. At this point, your system will begin to turn into a snowman. You will overload the pulse tube cooler. You will get water all over the lab. You will certainly look like a fool. So don't be a fool, leak check before you cool.