That sounds interesting, would you be willing to elaborate? Could you walk into a medieval library and go to town with a quill? What portion of your skills would be transferable? Which ones would you have to learn from scratch?
The technology related stuff—search engines, statistical analysis, digital preservation etc would all be useless, and I'd probably have to relearn what ever the local equivalent to copyright law and all the legal aspects related to that is, but the cataloguing, archiving and indexing would remain the same, as would the customer orientated aspects of the job—finding out what information my patrons are looking for, finding that information, and distilling it so they can understand the options available to them.
For example, say you come in, and you're doing a study on anatomy, and you need books with anatomical diagrams of hands. Well I then need to look up all the relevant texts in the medical science section (and because this is a medieval library, most of the texts will be in greek or latin, and maybe if I'm lucky we'll have some more modern ones in german), find those texts, find the information in those texts, judge if it's appropriate for my patron's needs, and then arrange for a copy to be delivered to them.
There's a Neil Gaiman quote I'm rather fond of: "Google can bring you back 100,000 answers. A librarian can bring you back the right one."
At its heart library science is the study of how to do research and how to manage information. Personally, I think it should be included in the study of every degree as managing information is kinda important in many fields. For example, there was this woman on my course who worked for a major Malaysian bank—they had paid for her to fly all the way to the UK to get a degree in library science because they needed an information specialist to manage their financial data. Large law firms will do the same, there's a reason why Canada built a legal library inside the same building their parliament meets in (the Library of Parliament, Ottawa, for those who are interested), and after my degree I strongly considered joining the NHS as an Information Officer, whose role is to know exactly what everyone is trained in (and keep that training up to date) so the right specialists can cooperate together on the right cases, and to ensure that when doctors retire all their knowledge is preserved in a process called "knowledge harvesting", so that retirement doesn't result in a loss of expertise. That's less about having the right books and journals on hand than it is about managing the information in peoples heads. (There's an argument to be made that people
are information, and that managing information is no different from managing people).