I can't speak for anyone else, but in my own case I vote 'yes'.
I don't want Cyprus to be part of 'mother Greece' or anything like that, but I identify with and love Greek culture, and I think it is important to maintain this cultural heritage. I was born and raised in the UK but I'm proud that my parents exposed me to Greek (and Cypriot) culture and kept it in my life, rather than trying to make me forget it and be a Brit.
I don't know about all the DNA stuff, I think that just over-complicates things. If they could do enough DNA tests on the appropriate people, we might all be descended from ancient Africans.
So to describe it all, I'll just borrow a phrase from Bruce Lee:
Being Greek 'is like a finger pointing to the moon. Concentrate on the finger and you miss all that heavenly glory'.
Personally, I don't care about 'how exactly' I am Greek, I'm happy and proud just to be Greek and enjoy the culture in the same way that I am proud of the distinctly Cypriot aspects of my heritage.
If some people don't feel the same then fair enough. Let them be whatever they are happiest being but I'm not giving up my heritage any more than I would force 'Greekness' on someone who doesn't want it.