ARM Option B hardware could be useful in deflecting an asteroid, but probably not by the methods you propose or the current Option B mission profile.
First of all: Picking up 50 ton boulders is going to have a minute effect on an asteroid massing 1,000,000 tons. Placing the boulders somewhere else on the asteroid will move the centre of mass (by a tiny amount) but that probably won’t do much good. Shifting the centre of mass does mean that the asteroid has moved, but unless we can shift the asteroid hundreds or thousands of kilometres we still have an earth intercept trajectory.
The other problem is that many asteroids don’t have enough easily detachable boulders to make up a significant proportion of their mass. Even if 20% of the asteroid is boulders, that’s still 800,000 tons of asteroid we can’t move. So flinging the boulders away isn’t going to solve the problem. (The other, bigger, problem with this approach is the horrible amount of propellant we’re going to waste slowing the spacecraft down and returning to the asteroid after we release each boulder)
There was a good discussion of using the Gravity Traction deflection technique (which is similar to what we’re discussing) on the NasaSpaceFlight forums a few weeks ago. Although the thread has since been deleted, in summary it concluded that the only situation in which Gravity Traction deflection would be the best solution (and more efficient that just pushing the asteroid) is when the asteroid consist of multiple smaller bodies (boulders) that wouldn’t have the cohesion to be pushed.
So in that case, where the asteroid is nothing but boulders, it’s quite possible that picking and throwing each one individually might be a good solution.
However, the significant metric in asteroid deflection (and in fact all orbits) is velocity. So the best solution for solid asteroids would be to use the propellant we have on board to push the asteroid like the full redirect Option A.
We might not need the fuel load of Option A to deflect the asteroid, after all we aren’t looking for a stable lunar orbit like the full Option A; we just want a few millimeters/sec of Δv to push it out of the way of Earth.
I can't find any Δv numbers of the ARM Option B missions, but if you can find them it would be relatively easy to estimate whether Option B would have sufficient Δv to deflect your 1,000,000 ton asteroid enough to miss Earth.