If the person she wants to add is in ChexSystems, she will not be able to add that person to the account.
Because that person has an outstanding balance with a bank (reason they're on ChexSystems to begin with), it's probably not a good idea to open an account with that person anyway. If they left the bank without making good on a bad debt, they may do the same thing with your mom if allowed to be on the account....not a good idea.
If the person only wants to cash an IRS tax refund check, most any bank will let you do that without having an account with that bank, as long as they present 2 forms of ID. They will also require a thumbprint, but the check can be cashed without having an account at that bank.
For any other kind of check, as long as you go to the bank the check was drawn upon, you can cash those checks as well without having an account, as long as you provide two forms of ID and a thumbprint.
Worked at a bank for 4 years.