We should not think about Luttwak's outdated theory, if somebody talks about an in-depth-strategy. Actually I like the term "Defense-in-Advance" mentioned above.
You first heard it there folks
You may call this an in-depth-strategy. But it is far away from Luttwak. Because this approach is an offensive in-depth-strategy and not a defensive one. And the combat zone is the newly conquested area and not the roman provinces.
I agree that it would be the first move, but Romans would probably quickly absorb these clients.
Clientelisation went a bit out of fashion in the Ist century, with Rome began either tightening its grasp or outright absorbing its clients (as Nero or Trajan did, for example), and I'd see these client tribal states being absorbed as they were in Roman Britain eventually.
But while western Britain had pretty obvious borders and no real potential destabilizing threat outside Picts, it would be more generalized along transrhenan Roman Gaul, forcing a more tight control of these clients until their full provincialisation (trough sheer control or after a revolt), which would be in line with the aformentioned general trend.
Eventually, it would mean for Romans to advance their direct military presence further.
However, something like an in-depth-strategy was not fully unknown to the romans of the principate, and not an invention of the late empire.
Not fully unknown but not really implemented, and mostly trough urban garrisons which may be a problem with a less romanised Rhineland, even without considering that these urban garrisons eventually turned more as auxiliaries of old, as in policed forces.
My point isn't that it couldn't be develloped, but as I said earlier that it would require some out-of-the-box thinking when roman geostrategy had different trends (and especially without the Barbarian pressure that forced partial, but not really that deep, geostrategical chances in the III/IVth centuries).
Again, not impossible, but it wouldn't be an obvious logical outcome of a transrhenan Roman presence to me.
About as long as they held Caledonia after their victory at Mons Graupius?
For once, I'd favour the contrary approach : Caledonia was but a remote and far point for Romans, without any benefit conquering it than local geopolitical purposes (that IOTL pointed as not being essential). Eventually, as political matters in Rome made Agricola coming back, it wasn't seen as a big loss (and actually making a "diplomatic" point to Picts)
Western and Southern Germania, on the other hand offered more prospects, geopolitically or ressource-wise. The main problem being the defensibility of these regions compared to Rhine, hence a more important military and clientelisation effort IMO.