yes. to help clarify 999-99-0001 is senior to 111-11-9999.
Yes your seniority in class matters years down the road when you and your new hire class mate are in the same seat in the same base, or bidding for the same seat in the same base. but there is not a thing you can do to change your seniority in class since your SSN was most likely assigned well before you ever started any flight training, and if you don't have a SSN when you get hired then good luck requesting a Low last 4 on whatever government document they use to determine your seniority. Don't worry about it, it is what it is. You'll find out your seniority when you see your name plate somewhere in the room in new hire training and the only thing you can do to improve your seniority is get a cadet date ASAP, be a ramper or gate agent or cross utilized agent, or even a flight attendant ,while you're waiting to start class, or to start class earlier.