No. They require you to be looking for another job. Plus, unemployment is for people who can't find work, not people who chose to leave a perfectly good job.
Unemployment Compensation is basically based on three things:
You are not working "through no fault of your own" (you were fired or laid off)
You are actively seeking work, and available for work.
You have not turned down work offered to you.
To quit for school basically disqualifies you in all three areas because you were not fired or laid off, are not actively seeking work - and are not making yourself available for work, and you essentially have turned down work offered to you in your current job.