If they managed to get adamantium onto Banner's skeleton (somehow repressing the change like they tried to do in the movie), and then allow him to become the Hulk - would this stop him from growing (bone wise)?
I will admit that this is an interesting question.
In the Ultimate Universe, Ultimate Hulk has broken adamantium. I'm not clear if he can in the current canon for the mainstream Marvel Universe.
My expectation is that it would NOT stop a Hulk transformation. As Banner's bones grew, they would strain the adamantium. They would be compressed. The spine is adamantium-coated as well - it would likewise be compressed. During the first transformation, Banner/Hulk would be in immense, crippling pain - very little compares to having your spine compressed, pain-wise.
At some point in the transformation, Hulk would take over. Bones being compressed wouldn't limit Hulk's mind - it would still surface. Hulk's mind has consistently had a single reaction to pain. When Hulk is in pain, it makes him mad.
The madder Hulk gets, the stronger Hulk gets. Typically, the stronger Hulk gets, the bigger Hulk gets (to a point).
I expect that after a seeming eternity of pain (during which Hulk would surface and become extremely mad) Hulk would become strong enough to shatter the adamantium bonds on his bones. They wouldn't go all at once, but in sequence. I expect Hulk would even beat his own body, providing more pressure on the adamantium.
He would then be walking around with adamantium shards embedded in his muscles and flesh, jabbing, cutting, poking. I can't imagine how much pain this would cause, or how angry it would make Hulk.
Past a certain point of rage, anyone's thinking, reasoning mind just stops. Even more than normal, adamantium-razor-filled Hulk would be a beast of instinct. He wouldn't understand what caused the pain, and would lash out at anything he could.
That Hulk might just crack the world in two.
Alternatively, it's much more likely Banner (who lacks a healing factor) would die during the process (which would most likely trigger a transformation instead). Hulk would then either smash his way out of the tank (and not have adamantium) or get his very own, Hulk-sized adamantium skeleton.
If Hulk had an adamantium skeleton, it would threaten to break free from Banner's puny body whenever he started to change back. That would either cause him to revert to Hulk status or make a BIG mess. Either way, it wouldn't be pretty.
Besides making an interesting thought-experiment, the answer would be: No. There would be no way to make it safe enough for Banner to survive the bonding process. Without regeneration, he would die on the table or revert to the Hulk, stopping the process.
Banner could never survive the initial process. The adamantium bonding technology is supposed to be lethal to anyone without extreme levels of regeneration and even with extreme regeneration, it is still killing the subject (in the case of Wolverine, it is reducing his regenerative abilities).
While the Hulk possesses the regeneration capacity his body would be likely to reject anything that was not a part of him, since his superhuman immune system would deem the foreign material as "not Hulk" and expel/repair his cellular structure minus the offending material.
Since the Hulk's regeneration processes is even faster than Wolverine's, it is unlikely the process would even be usable on the Hulk unless his metabolism could be greatly slowed to prevent the rejection process. If somehow it could be done, it would prevent a transformation back to Banner without killing him during transformation.
Ultimately, why would he need an adamantium skeleton?
Without it, he has already proven he is one of the mightiest mortal beings on the planet. It would be like adding gold electroplate over a brick made of gold. It would bring so little value to the Hulk's capabilities as to be not worth the effort to do it.
When your adage is "the Hulk is as strong as he needs to be" or "the Hulk has the capacity to split the crust of the planet, extinguishing all life on Earth" except maybe for himself, what else could he need?
In the Marvel Universe, in terms of damage resistance and damage dealing, he is already, "The Man Who Has Everything."
If Banner were stuck as the Hulk and the adamantium bonding process took place while the Hulk was the Hulk, then that would be interesting. There have been periods where the Hulk took over and never transformed back into Banner for a long period of time.