Does sepsis usually cause oxygen saturation levels to fall?

It can. Sepsis can cause acute inflammation and swelling in the lungs making it harder to breathe, and causing oxygen levels to drop. Compromised heart and kidney function, as well as fluid resucitation can make matters worse.
Yes. Sepsis is the body's generalized inflammatory response to a specific infection. Even if the actual infection is not in a patient's lungs, many patients will experience lung injury due to the inflammatory response. The blood vessels also become "leaky" during sepsis, so edema can build in the lungs and further impair oxygenation. For severe sepsis, a breathing machine is not uncommon for a time.