Usually worthwhile, removing the ground with the pick is extremely quick compared to mining the copper. Sometimes you find a second ore vein that's mostly or completely buried near the first, or find out the ore vein was a lot larger than it looked. We just mined out one in my MP game yesterday, and made sure to dig down and find as much as we could. We got a full stack of 30, plus about a half stack more. Didn't take too long, would have been faster but mining generally brings lots of greydwarves. I think it was very much worth the few minutes it took to uncover the additional ore since we built a tiny structure with a workbench, fire, cooking spit, and some storage right next to it so we can refresh the rested state, and store all the rocks, ore, and drops from the greydwarves.

If you just go mine a bit and move on then I'd say don't bother, if you set up a small mining camp, especially if you're close to two or three ore deposits, then it's more likely to be worth the time to dig it out.