I'd be afraid. To be safe, you'd have to be certain that from the time you quit until the day you get let go from your full-time job that you'd earn 5 times your weekly benefit amount. If anything goes wrong and you don't earn that amount, you'd have to worry about the reason why you quit the part-time job.
You won't be denied because of your part-time job. You'd only be disqualified week-by-week if it pays you too much, or you get fired for misconduct, or you quit without good cause.

