Even though becomes even so at the begining of a sentence?

[Unregistered]

Is it true that if you start a sentence with "even though", you can also put "even so" instead?

 

[Anglika]

I don't see it as grammatically possible:


Even though the duck could swim, it drowned [makes sense - The duck drowned even though it could swim]
Even so the duck could swim, it drowned [does not make sense - The duck drowned even so it could swim]

I think the answer has to be no.