I actually expect them to route them towards Earth, to some stable orbit, to be mined. But yes first the collision protection, that's much simpler to achieve and important
On the other hand, getting a near-miss asteroid to orbit Earth instead means taking it from above escape velocity (11.2 km/s) to an orbital velocity, which means at least a thousand times more delta-V (more like 4 km/s). And that's the easy case -- getting an asteroid from the belt to fall toward Earth is another several km/s on top of that. Besides, ejecting 1M kilograms into a busy Earth orbit in order to slow the asteroid down sounds like a pretty scary idea. Especially since we'd have to do it hundreds of times for one asteroid.
So no, it wouldn't be the same technology at all.
And if it's the former, giving it a small bump is just as likely to put it on an actually-collision course as not doing anything at all.
There’s at least a plausible need there, what with the whole “don’t want to slam an asteroid into the planet” problem.
Mining is still an utter fantasy. It’s completely economically unviable to mine anything from an asteroid and bring it down the gravity well, and we have close to zero ability to actually mine and manufacture anything in space. We are a long long long time away from that.
That said; what the bigger issue - for in situ operations, the distance to get the raw materials or just doing anything with the raw materials at all? Is it going to be - we could do anything at all but going all the way past the orbit of Mars is too much trouble - or - Getting to a rock past Mars is easy but it's hard to do anything practical with it (compared to just getting it off Earth presumably)
I got no clue as to which way it could go but it doesn't seem a question that answers itself to me.