As long as you have sufficient funds in your checking account to cover the cashing of the large check and the bank has enough cash on hand to provide to you when you cash that large check then yes you can cash the large check at the bank.
It's best to call the bank ahead of time to make sure they have enough cash on hand to be able to cash the large check for you.
If not then you'll have to deposit the check into your checking account and wait 3 to 6 days for the check to clear and for the funds to be available in your checking account.