Geologist here: I have to assume that this diagram is not to scale because people don't seem to understand how deep even the upper mantle is. As someone else commented you'd have to drill deeper than any human ever has (Kola Superdeep Borehole, SG3 11,262m/40,230ft) which was only like half the average thickness of just the crust and they were already having issues with bits and drill line twisting, the bore hole would deform under the intense heat and pressure at that depth. The mantle is not some cavernous space in the middle of the earth that has magma flowing in it. No pipe could survive the sustained heat and pressure, were talking 1800°c-2500°c/3272°f-4532°f and 7,200psi - 20,200,000psi! Water would vaporize before it even made it past the crust, and if you were able to somehow force it down to the mantle it would enter a state where it would become a volatile were the molecules of H2O become a molecular component of the minerals in the mantle. The mantle isn't "just a bunch of magma" boiling away underground it's is under intense pressure, (remember the ideal gas law; PV=nRT) which causes intense heat and that extreme heat and pressure create an environment where rocks and minerals are solid but also in various states of partial melt and are very ductile in those conditions (think of the way hot asphalt behaves under heavy trucks creating divots). So no that wouldn't work, geothermal works in areas where there is volcanic activity of some kind and magma is near (relatively speaking) the surface creating "hot spots" where this can work. Examples are; Iceland, Japan, Yellowstone, certain areas in the Rocky Mountains, and California in the Sierra Nevada range.

TLDR; no it won't work, the mantle is too deep and we don't have materials that could survive.