Maybe? Doesnt make sense to me:
So let's assume Roger and his crew, or Shanks very early on, visited Little Garden (as otherwise "old" probably doesn't make sense)
We see Shanks during the East Blue Saga in East Blue, that means he was easyl able to check on them going through rivers mountain as its very close to Little garden.
This is also about the same time the Strawhats Pirate meet the Giants. And they don't receive any news about them for almost 3 years yet not one of them thought they were dead
And Mr. 3 told us no one heard about broggy and dorry since they started their duel 100 years ago. So there was no world news concerning them being dead in any semi-recent times.
Also, we know from Oimo and Kashi that the giants pirate dissolved after they left Dorry and Broggy behind on little garden, so their location never changes.
Shanks seems to allied with Elbaf of giants, so even if he would go there and ask, they would refer them to Little garden
I personally don't see how Shanks logically ever thought they were dead