As long as you weren't hired to work any specific shifts outside of your planned availability, I don't see why not. However, you may be on track to getting no hours at all considering more senior employees are likely to get earlier shifts they want before you do.
It should be possible, however you should build good relationships with your supervisors and managers. If you need to limit your availability, being on everyone's good side is a huge plus. You can't do much about higher seniority people because they have the ability to claim your shift if they need the hours, but if you work hard and stay on your supervisor's good side you should be fine.
