I would guess it is possible to catch cod from around the immediate area of the Needles, but virtually all cod fishing in the area is done at anchor. Anchoring anywhere around the immediate vicinity of the Needles is difficult, dangerous, and perhaps even not allowed (shipping lanes). So, you don't see much Cod fishing there.
As you say, it is used more as a general land mark for other cod marks.
I'd say it was worth a go, though. The cod do make their way into the solent from the open sea, so they might rummage around the rocks for crabs on their way in. Wasn't it last year that someone found a cod in a rock pool on Portland Bill??
BF