Just don't walk in 10 minutes before closing time and expect it to go smoothly. They will definitely check the cheque writer and if the issuing bank is closed it may not be accepted.
Just have your license with you and go sometime while the bank is open and you should be fine. I don't believe the online store accepts checks though, which I find odd as they do accept debit cards. That's actually quite the pain because my bank has a $1,000 daily limit on debit cards, and if you have a purchase that is greater you have to go get it approved. Thanks for making it more difficult than it needs to be Apple