Yes, that should have caused him a lot of pain. The adamantium would have protected the 'bones' (and I preferred it when the claws were just implants from Weapon-X) but they would still have hurt quite a bit.
One example I can think of off the top of my head is all the times Logan has cut through a Sentinel. Now obviously, those metallic behemoths must be made of some pretty strong metals to support that weight. Logan is stronger than the average human, but not by all that much. Now try to imagine this scenario. Say you have a really sharp knife that absolutely will not break, no matter how hard you hit it. And you take this knife and swing it as hard as you can against a big piece of steel. Would you cut through the steel? No, you wouldn't. But how is your hand going to feel? Good luck keeping your grip on the knife.