I don't know if 'feeding expansion' is necessarily the right way to think about this, but by the first Friedmann equation, loss of photon energy will in fact be balanced by the increased expansion rate...
Sure, though the first Friedmann equation, or any other equation, where terms are balanced, e.g. a + b = 0, doesn't tell you anything about causality, though redshifting of light is exactly caused by expansion, so it is not strange that both are "balanced".