Speaking more generally it wouldn't surprise me to see Bethesda adopt id's engines some time in the future but only if they can manage what Bethesda needs in terms of large open worlds.
Or if Bethesda decides to change their policy in some titles and, for example, use a node system (if
too vast and open can't be supported).
Not counting on it, though, but I think it would be refreshing for them as much as to the audience, if they slipped a bit from their norm with certain franchises so that not each of them would offer the same thing with just different wrappings.