The right to be called a 'pure' Jew passes through the mother, but in terms of genes I don't think it matters.
I wouldn't be surprised to hear that the lost tribes of Israel turn up at some point. There have been some interesting claims. The problem I have with the proof text provided from Duet is that the prophet in question seems highly unlikely to be referencing an American president. Christians say a 'prophet like Moses' is Jesus.
The biggest problem I see in trying to track the missing tribes concerns the assumption that somehow they would still be intact, somewhere, ready to be discovered. The presence of Jewish communities throughout the region shows that many did retain their identities- indeed, they retained them to the present day- but there would still have been a heck of a lot of assimilation, too.
It might be an interesting historical fact to throw to my two secular atheistic friends posting on this thread that the promised one was said to come from the line of Judah as far back as the book of Genesis, which I hope no one disputes was around for a long, long time before the dispersions began (quibble with me over Isaiah, but please, dear gawd, not Genesis). Quite the coinky-dink that of all the tribes of Israel to be dispersed, only Judah and Benjamin were dispersed in such a manner that they could return to their homeland as cogent whole, preserving the possibility that the messiah could yet arise.
Sure, ok, the odds are 1 out of 12, I reckon, but really however you slice it, is it really just plain luck all around that Sennecharib turned around in 722 BC?