Of course, water vapor is a major greenhouse gas, so this isn't going to calm the fears of the global warming crowd. Also, experienced firefighter will affirm that in superhot fires (around 2,000 deg centigrade) you can't use water to extinguish the blaze because the heat will separate the hydrogen and oxygen in the water molecules. Not sure if magma gets that hot, but it could be another unexpected consequence.
If they can somehow 3D print titanium pipes into the magma, sealed real good, the water running would exchange the heat.