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Yes it will. Being an AU adds the account to your CR just as if it was always yours.
It is usually positive. The only real peril to you is that if the %util on the account goes up, or future lates are accrued, it will affect you, and is beyond your immediate control. Being an AU requires a lot of trust in the account holder.
As for what CRA it is reported to, that is totally up to the OC. They can report to no CRAs, just two, or all three. Most major CCCs report to all three. Is the account reporting to all three CRAs on your grandma's credit report? If so, maybe the OC did not notify all CRAs of the AU addition.
How long a closed account is included in FICO scoring of AAoA is totally up the FICO programmers and up to the CRAs to determine how long they include it in their files. It is unregulated under the FCRA. From what most say, they normally remain for 10 years from date of closing, but can drop sooner.
They wil normally retain it for a minuimum or 7 1/2 years to ensure compliance with the reporting periods of FCRA 605 should issues later arise on the account.