You can´t imagine how many times Turks have asked me this. I am surprised how well Turkish people know the specialities of their own language. Finns generally do not bother their heads with such things.
I am not a specialist but because you ask I answer: no.
The most important reason for me to think this way is - as you suggested, gokuyum - lack of common basic vocabulary. I think the syntactic similarities between Finnish and Turkish are language universals which to some extent show in all agglutinative languages. They are amazing enough though. No wonder the tools used in language planning are also very much the same (that is why kuyruklu yıldiz = pyrstö|tähti).
And anyway, if there are common roots they are so deep in the ground they have no practical meaning. I am not learning Turkish easily (if that is what you think).
I am not capable of analysing my own language learning but I get an idea when I listen to my Turkish teacher Hatice hanım who speaks excellent Finnish. I analyse her speech constantly: I know why she has difficulty pronouncing our diphtongs, I know why she uses certain pronouns in a peculiar way... But one thing especially has attracted my attention: she is not afraid of long words which other learners of Finnish always complain about, she jumps into the system of word inflection just like she has always been there. That is because she has.
