We now know that only Eldians can turn into Titans. We also know that the Coordinate doesn't work on Asians and Ackermans (and other unnamed clans). This implies that that the Coordinate only works on Eldians. If we accept this, the fact that Asians and Ackermans cannot be affected by the Coordinate means that they are not Eldian in origin, and so cannot turn into Titans.
Since Mikasa is half Asian, half Ackerman, both bloodlines which cannot be affected by the Coordinate, does it mean that she will be unable to turn into a Titan if we use the serum on her?