OK, if you want to split hairs, I will modify my statement to "If you find an organism ON EARTH that does not have nucleic acids as its genetic material, then evolution is false." Better?
Actually, if such a creature were found, it would only argue for multiple beginnings of life, rather than a singular beginning.
[A "singular" common ancestor is actually an argument for Biblical Creationism, which unfortunatly religious people reject because it then acknowleges the evil "E" word]
Also, certianly an argument could be made that extreemly early life split into two major forms and the common early ancestor is no longer in evidence.
No, it's not. Your test of falsifiability is not credible.