Does pregnancy cause forgetfulness?

Yes. Yes. Some people call it "pregnancy brain". Its a little annoying but transient and resolves after pregnancy.
Yes. However, I guess that the often reduced sleep and increased fatigue from the increased physical demands of pregnancy may give one the impression or fear that the dreaded "pb" exists. So one never knows...
No. If you are speaking of the post - delivery amnesia, then probably yes. However, neither during my own pregnancy, nor in 24 years of practice, had "pregnancy brain" ever been even considered. Females that I have known have generally performed exceptionally well during pregnancies. I am not aware of any evidence that "pb" exists, but I do know that it hasn't lead to car insurance rate hikes.