OP's analogy is flawed/incomplete.
What you're meaning to ask, essentially, is whether specialisation in academics would enhance somebody's potential for generalisation more so than would be the case for a generalist trying to turn to specialisation.
I guess the problem with this line of enquiry is pinning down precisely what a generalist is in the context of academia. What is the academic equivalent of a cross fitter, if you will?
Even so, notwithstanding these difficulties of classification, I think the answer is clear: somebody who has specialised and attained a deep knowledge in one particular subject, is probably more likely to be able to easily and more rapidly acquire a general understanding of many subjects, than a 'general knowledge expert' will be able to turn his mind to the deep understanding of one subject.
I think the reasons for this are obvious.