yes you can, you can literally animate anything in maya, but it is a sudden key frame and maya doesn’t show the key frame on timeline for some reason, but for example you made 2 key frames one at frame 1 for xyz order then another key frame at frame 53 for yzx order, it not going to change gradually because it is an order what do you expect? but until frame 53 it uses xyz order and after that is yzx.
i never have animated something in this way and with gimbal lock problem on the way you should be careful about any inconsistency that it can bring to animation.
but capability yes, you can even animate file addresses.
and it supposed to be an order in general, it is just merely a maya feature that you can literally animate everything but this does not mean that some features are supposed to be animated