I was wondering the same, and have nowhere seen any comments/tests. In general, higher temp means faster aging, a simple law of physics (arrhenius law). aging means drift. that is in line with the temp setting observations of the 3458a ltz1000. of course, always, there are additional effects. the ltz, according to the data sheet, needs some time to settle and decrease in drift rate. and of course, there are more and less stable devices. it is beyond me why a 3458a opt. 2 may or may not be powered and still meet its accuracy while all precision references must be on. also, this is a little bit like saying if you have a precision test equipment, keeping it on is better. in my experience, the opposite is the case. of, course, not the exact same thing, and not as simple as that, but anyway.
it woud be worth while doing a test with a set of ltz1000, keeping them on initially until stabilized per data sheet, determining their drift rates, and then switching some off. i bet there is not much difference, maybe the ones in off-state are even more stable, given their initial drift is already over.