It’s complicated. Rock, you see, is illegitimate. His mother raised him in poverty (as I recall). When she died, he was left on his own – much as Terry and Andy were, and even their adopted father Jeff before them. He’s never really known Geese in a significant way, and certainly never been recognized. If anything, Billy is more of a son to Geese than Rock ever was.
Ignoring the Art of Fighting time-shift, the KoF timeline seems to diverge from the Fatal Fury one after Fatal Fury 3. FF3 is where Terry adopts Rock.

http://www.vgmuseum.com/end/neogeo/a/fatal3terry.htm
As others have said, Rock does pop up with Terry (albeit way, way too young) in Kof2k1, and occasionally in the off-screen storylines accompanying each game. And the Ash-era games, of course, tried to transition to the Mark of the Wolves timeframe, which should have been happening chronologically around then.
But, Geese seems never to have died in the KoF timeline. There was no Real Bout, or Real Bout didn’t end the same way. This was ambiguous for a while; aside from KoF’96, which came out the same year as Real Bout, Geese was absent from the series for years. When he was referenced, it was with a wink, suggesting that he was dead. Then, out of nowhere, Billy’s story in KoFXI 2003 directly involved Geese, and hey presto, officially he wasn’t dead! Apparently he never had been. Which is interesting, considering the previous ongoing effort in transitioning KoF into Mark of the Wolves territory.
EDIT: 2003, not XI. I often mix up the character rosters for those two.

http://www.vgmuseum.com/end/neogeo/c/kof2k3out.htm
Nothing that we’ve seen in KoF depends on Geese having died. Rock was already living with Terry anyway; presumably his angst takes a different form with his real dad still alive. I’m sure that Hotaru would still be searching for her brother whether or not Geese was in the world. Geese holds no bearing on Tizoc’s antics. And so on.
But, really, KoF’s handling of the Geese issue is inconsistent at best. You can easily slap mental bandages over the inconsistencies and say, okay, this can make sense – but it’s not worth pretending that it does on its own. It’s just best to take each game on its own and say, okay, at this moment, these seem to be the assumptions at play. They may not match the assumptions in the previous game or the next one, but they’re what’s happening now.
(Then we also have the Max Impact series, which is its own continuity apart from either Fatal Fury or KoF, but seemingly much closer to Fatal Fury.)