Although there is no reason why AHP can't be used for making decisions in UX design to prioritize tasks or requirements, I think you'll find that the level of analysis required and the output generated isn't necessarily the answer that you want.
Instead, there are simple strategies or processes that will give you the high level buckets (e.g. MoSCoW process) that allows you to narrow the focus and therefore the complexity of the analysis and decision that needs to be made.
I don't know of any examples or projects where this has been applied, but given that it is not too dissimilar to other methods I can imagine that it has been applied somewhere.
If the complexity of the analysis is prioritizing the tasks or requirements in the context of UX design only, then I think AHP might be an overkill. However, if it is about weighing UX considerations in the context of other business or technical constraints then you may consider more complex analysis processes.