I've got 2 considerations here:
1 - From the perspective of your risk assessment and supplier approval controls, both sites operate the same or similar systems and procedures... But only one of them is subject to 3rd party verification audit. This is very significant, especially when it comes to auditing your systems - if supplier approval is done on the basis of GFSI-benchmarked certification then it is completely irrelevant whether an uncertified site shared its name or processes with a certified site, if it is not itself certified.
You can certainly approve one of these sites based on GFSI-benchmarked certification, but the same cannot be said for the other.
2 - You are generally required to approve your raw material suppliers, but not the suppliers of your suppliers. If site A manufactures a raw material that it transfers to site B, and you purchase materials from site B exclusively then it doesn't make any difference to you whether site A is certified to a GFSI-benchmarked scheme or not (this is purely from a compliance point of view, you may voluntarily risk-assess your supply chain as far back as you want to go).
Conversely, if site A is certified to a GFSI-benchmarked standard and they transfer material to site B and site B is not certified, it wouldn't make any difference to your risk assessment that site A was certified because your supplier (site B) wouldn't satisfy your approval criteria.
To make this very simple, a food group may have 10 manufacture sites, of which 8 are certified to a GFSI-benchmarked standard and 2 are not. You could state very clearly which of those sites met your approval criteria and which didn't, and it would make no difference if you were told the 2 uncertified sites followed the same procedures as the certified sites. Your approval system could not note their BRC site code (because they don't have one) and nor could it note the expiry date of their FSSC22000 or IFS certificates (again, because they don't have them).
It would not be possible for you to demonstrate compliance if you were to extend approval to the uncertified site simply on the basis that it operated tot he same procedures as the certified site.