Yes. That's what's been shown so far.
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Y-DNA is something you inherit no matter what from your father. If your father was from China with a typical Chinese Y-DNA marker 2k years ago, you'd still have it. It's useful for looking at migrations of populations with different Y-DNA distributions, but not at all useful on an individual basis or between populations with similar Y-DNA distributions. I2a and R1a are undoubtedly not native to the Balkans before the Slavic migrations, we know that anyone who has either of those haplogroups in the Balkans has paternally Slavic ancestry if you look far back enough. We can't tell what affects this has had on appearance after hundreds, maybe more than a thousand, years of mixing.