Even in our pre-democratic days, they had to be in parliament, though not necessarily elected (often they were Lords).
It would in fact be theoretically possible for an unelected banker to become PM, if he were first appointed to the House of Lords and then selected as leader by a Party. I think it's fairly unlikely, however. As recently as the 1960s, a hereditary peer -Home - was chosen as Tory leader, BUT he was expected to resign his peerage and seek election to a parliamentary seat.
I just had a look at the Greek constitution:
http://www.hri.org/docs/syntagma/artcl25.html#A3 It says that 'the form of government shall be a parliamentary republic'; but it doesn't seem to specify details at that level, unless I'm missing something. So I suppose it can be interpreted freely.
Of course we don't have a constitution at all, so....