If I interviewed you and you told me you were going to work 2 FT jobs, I wouldn't hire you. Most of the people I have hired can't handle 2 part time jobs. They either can't keep the days straight and don't show up, or they get sick a lot, or they call all the time trying to get the shift off. Read the posters on this board, geez they can't take 3 days, half of them, it's too much stress, too much drama. checkout clerk, sure, you can do 72 hours a week. This is way different.
So long story short, if they didn't ask if you were going to quit the other job, it isn't implied. They just expect that you're not going to kill yourself. Although you do have noble blood for wanting to exact this on yourself. I wish you well, whatever you decide.