Interesting question. Not sure of the validity of the notion that his Divine Will was asleep —but it sounds poetic enough
to be humorous —but I think I get the point.
I tend to say his divine prerogatives, as we would consider them —his attributes of omnipotence, omniscience etc, but, again, 'as we would consider them', and no doubt as we would use them if we could— were not used in those ways we consider them. Your word, "suppressed", is a good word for it.
Yet the whole of his time here, his omnipotence
is displayed, in at least these ways— that he lived as a human without sin, without shrinking from his commitment, without any hint of personal selfishness, and, (probably my personal favorite to go on about), by "skating so close to the edge of disaster (total failure) without going over the edge" which (to me) demonstrates the infinite power of God so well, accomplishing the 'impossible' what he did by the mundane, the apparently senseless, (even using the 'wrong' men for his purposes), and depending on the Father for everything.
In Sunday School, I have illustrated something about the infinity of the power of God by principles in hydraulics and electricity, (drawing on a chalkboard), and by comparison with my little daughter to myself. If my daughter, (at the time about 4 years old, I'm guessing), was to be able to break a stick in her bare hands, when it finally broke the pieces would probably fly out of her hands across the room. But if I was to break the same stick, being much stronger, it would not take the same straining to accomplish it, and there would be little excess motion. Likewise, from a tank of water, the depth of the water and the quantity of it are all the pressure and capacity the system has available, that runs down a pipe through a valve. The pressure, resistance and current are all limited, and can only do so much. Same goes for electrical circuits.
But with God, there are no limits, and so no excess motion. He can "valve" it all he pleases; he can dance at the edge, without overbalancing! I could go on and on with this picture.*
But in fact, it is much more convincing than even that, because all things began with him, and he knew them all before creating, and caused them all for his purposes and for his own sake. We can know that the Christ could only have been God, at least by that fact, if not by the several other ways we can know it is so.
Maybe this seems to wander off the topic of the OP, but I don't think so. It is, at least, a side issue to be put to rest, that though it might seem otherwise to us, there was no possibility of failure on his part, and that the very depth of depravity —rebellion against God, the creature calling the Creator a liar and irrelevant— had to be slain by his death.
*This picture is too small. His ways are not by immense power —at least, not as we define it— but if he can dance at the very edge, it is not by infinitely precise calculation, but rather, because the edge is what HE made it, and is where HE put it. So it is OUR view of what he does that supposes he keeps choosing the wrong people for his purposes, and wastes so much effort and money, and does things so backwards and small. Note how the atheist demands an explanation, why God takes humanity through all this trouble to accomplish Heaven! And note how the self-determinist has to attribute what he can't understand God doing, to libertarian free will !