Yes and no.
No, it wasn't supposed to leak into the bilge - nothing ever is.
Yes, if you seal the leaks into the bilge, water can then leak into the cuddy (from where it drains into the cockpit and from there to the drains in the back, or pumped overboard). It's still a nuisance, but no longer a problem, because you can deal with it in the open. (I've sailed in a boat where that happened, and every hour or so, some bailing action was needed - no self-bailer on that boat. It interrupted the routine a bit, but it was manageable unlike if the same amount of water had been found in an inaccessible bilge. The cuddy was full of gear, the trick was to use truly waterproof bags for the bottom layer ...).
The only way to reduce that problem would be with some kind of foam/rubber gasket that holds back the water but lets the rope/cable pass. Not impossible to do, but won't be perfect.
About the picture a few posts above: looks like somebody used galvanized. That's not going to resist rusting. Best you can do is to regularly apply a bit of corrosion inhibitor (comes in a spray can).