Job hunting - schedule?

How badly would it affect my chances of getting a job (specifically, Walgreens, Winn-Dixie, Publix, retail stores, etc.) if I say I can't work before noon? I'm very, very terrible at getting up in the mornings. I do not want to end up getting a job where I will end up being late and cranky for work. Is it most logical to not check "open to 12pm" on the schedule section of an application, in my case? Or should I check all times and hope I don't get scheduled in the mornings?