Yes, with that persons permission and signature. You both would have to go to the bank and have you added and how it is listed on the account will also determine how the moneys can be drawn or...
It depends on the bank. Some banks will allow this and others will still deny. Generally they will do a background check for any signers on the account.
There are many banks across the country that provide accounts to people in chexsystems. I've linked some sites below that have more information about specific banks and lists of banks broken down by...