The use of the word "blackmail" is wrong. To join the EU 2 things must be true:
1)Fulfill the criteria.
2)Be accepted by all current EU members.
1 is the responsibility of the candidate country.
2 is more complicated because not always everybody agrees who should be accepted and who should not (current example is Turkey). While there where countries in the EU that would prefer Cyprus not to be included, we fortunately had a friend with a veto power within EU that used this power to convince the rest to accept Cyprus.
Politics are based on balance of power and how this power is used, and not on verbal promises by some politicians.
In this case it would be reasonable to assume that Greece will say to EU that we will not support the next enlargement that includes Turkey, unless Cyprus returns to pre 1974 ... and we lived happily ever after.
This is irrelevant because:
1)Turkey occupies Cyprus and not EU.
2)A veto for Turkish membership doesn't mean the removal of Turkish troops.
So in this case using the power of veto would probably not bring the desired results, and thats why we will probably not use this veto.
Still, we do have that power, and we can use it to our benefit.