Hi,
Welcome to the forum.
Most likely you should be ok, they process the 8822 forms very quickly. After they have your envelope, it takes them less than a week to process the Change of Address form. On the other hand, it takes weeks or even months to process your tax return and to send you a check.
If you really want to be sure, walk over to your closest Social Security administration office and have them change your address in their system. I believe these two systems are interconnected.
Your another option is to call IRS over the phone in about a week and ask them to confirm if they already changed the address.
Contact IRSGood luck.
Form 8822 Change of AddressAddress change notify IRS