Gravitational wave energy transport When a gravitational wave passes through a region of space (which may be, or may not be, empty), does it deposit energy (in any form) in that region of space? A frivolous version of this question might be: "Can I boil water by waiting for gravitational waves to heat it?"
 A: 
When a gravitational wave passes through a region of space (which may be, or may not be, empty), does it deposit energy (in any form) in that region of space?

If the region is filled with matter that has some form of dissipation then yes. Essentially this question (and answer to it) is the subject of Feynman's sticky bead argument:

Feynman’s gravitational wave detector: It is simply two beads sliding freely (but with a small amount of friction) on a rigid rod. As the wave passes over the rod, atomic forces hold the length of the rod fixed, but the proper distance between the two beads oscillates. Thus, the beads rub against the rod, dissipating heat.

If there is no mechanism for energy dissipation (or other form of energy storage) in this region, but it is not empty (for example, it could contain an isolated point charge and its bound  electrostatic field) then the incident gravitational wave could partially scatter and also undergo partial conversion to electromagnetic radiation without changing the state of that region after passing.

A frivolous version of this question might be: "Can I boil water by waiting for gravitational waves to heat it?"

If you have either a body of water that has a frequency of quadrupole oscillation modes coinciding with the frequency of incoming gravitational wave, and the intensity of that wave is large enough to cause dissipation from nonlinearities of resonant oscillations. Obviously, for Earth-based bodies of water (from coffee cups to oceans) there are no astrophysical GW sources that could transfer enough energy to even approach threshold of detection.
But if we for example consider a star in the same system as a black hole binary, absorption of GW by that star could have astronomically measurable consequences as considered here:

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*McKernan, B., Ford, K. E. S., Kocsis, B., & Haiman, Z. (2014). Stars as resonant absorbers of gravitational waves. Monthly Notices of the Royal Astronomical Society: Letters, 445(1), L74-L78, doi:10.1093/mnrasl/slu136, arXiv:1405.1414.

