I know you're not asking me specifically, but NO, absolutely not. Same thing with that Street Pass "accomplishments" stuff they do with 3DS. It's not meaningful unless you can access them WITHOUT booting up the game. And if you can see your friends' progress while snooping around, as well.
Xenoblade, although I enjoyed my time with it, the "achievements" felt pretty much like random bullet-points to extend the game. I think they gave in-game rewards like extra experience, or something like that, so they weren't totally useless. But as a general concept, they still were.
Even a launch Wii game like Excite Truck had in-game achievements. Again, cool, but why try for them if you get no bragging rights by showing them off, since you can't show them off. A random gamer score isn't as important as looking at your buddy and being able to deduce that he's pretty damn good at Excite Truck. Not that gamer score is an inherently bad thing. But nothing at all, outside of the game, is pretty lame.
Others may consider it all to be not important or shallow, just like those people may view high scores as unimportant and shallow. For others, it creates drive to finish the task. Nintendo's Donkey Kong is still played for high scores to this day, for example. The foundation of early video games was trying to out-do one another, creating a competitive setting.
But Xenoblade's several (and I think it's close to 100?) in game achievements, no I'd have no desire to try to do them all, regardless of the in-game kudos. If each game had some focused ones though, around 10 or so, it might prompt me to do whatever that game is asking me to do. Beat Super Mario 1 without Warping? Challenge accepted. But, so far, challenge not given... Beat Double Dragon II NES without the stage select? I might try to power through it. There's a lot of unused potential there, both in the e-shop and retail releases.
Even being able to grab a screen shot of an ending screen for title would be something, even if only for a reminder that the game was in fact completed.