No, they don't. I've never been asked to enter my passport number anywhere but on an immigration form. I've never signed up with that Clear Skies (or whatever it was called before it went belly up) - the only information that anyone would have would be the required information for traveling anywhere these days - name, birth date and gender. TSA doesn't have access to my American Airlines frequent flyer account to my knowledge. These days who knows who has access to what though but again, my passport number is not recorded anywhere in my AA frequent flyer or profile accounts.