I think the chief connection is that secluded mountain valleys would have offered protection and its no mistake that Elves built in such places: Rivendell and Gondolin hidden in valleys, Thranduil's realm in the deep woods, etc. That's why a lot of Abbeys and other similar communities were built in hidden places (Fountains Abbey is a good example in North Yorkshire), especially given the frequency of invasions to the British Isles in the early years of Christianity.
However, there are two 'buts'. Firstly, what about those Abbeys quite pointedly not built in secluded places, even in the early years, such as Whitby and Jarrow? These two in particular were extremely important and yet seemed to be sighted as if to shout out "look at us! look at our power!". And secondly, the reason so many Abbeys are in valleys is just that there are rivers there and better pasture. Monks were also farmers and fishermen; in fact the majority of monks and nuns would have been engaged in the more prosaic work of food production, and they were probably glad as I've read many a time that the scribes lead awful lives, in constant fear of their superiors for spoiling manuscripts and with damaged eyesight and lead poisoning from inks.
I agree Rivendell probably sits with the idealised side of monastic life, but I doubt the artsy Elves we see in Tolkien's work would have been prepared to 'muck in' like real monks and nuns were, and are.
