If invocation without full attention were an “insult” to God, I’m afraid all but a very few of the saints and sages would be guilty. Who of the rest of us can make it through even a short session of formal prayer without the mind wandering and having to be brought back, wandering and having to be brought back … perhaps ten times in as many seconds? “Full attention” is a tall order indeed!

As you’ve already deduced, I would thus side with those who say that “invocation is beneficial under any condition”. Now of course, benefit is a matter of degree. Obviously a given repetition of the Name, or sequence of such repetitions, during which we are in fact fully attentive, or at least closely approaching that state, will prove of more value—not because of any difference in the power of the Name itself, but because we are able to assimilate and appropriate that power more fully or deeply, more organically.

The advice of those whom I trust on this subject is therefore to make the invocation a companion throughout the day, giving the Name as much attention as possible, but being confident that even when our attention must be directed elsewhere, or has been distracted elsewhere, the Name is still at work within us.