Only if "John speaks either Greek or Sanskrit" is (and in the same way). One interpretation of "either" is "one or the other, or both", and this would be most sensible if the context included something like "it just depends on who he's talking to". The other interpretation is "just one of these, but I (or whoever's perspective the discourse takes) don't know which". I think the point is that this latter "wide scope" reading is supposed to be equivalent to "John knows a man who speaks Greek, or John knows a man who speaks Sanskrit"; as opposed to "John knows a man who speaks 'Greek-or-Sanskrit'".

It doesn't strike me as ambiguous, but I suppose you could try to interpret it like this:

A) Either [John knows a man who speaks Greek, or John knows a man who speaks Sanskrit]
B) John knows one man, and that one man knows either Greek or Sanskrit.

It's unclear to me if the scope difference actually results in different truth conditions in any relevant circumstances (or indeed whether the scope change is even possible structurally).