Would it be efficient to use water as a coolant in a hydrolox rocket, then feed the steam after the water has boiled (due to heat transfer from the engine nozzle) into the combustion chamber, so as to add mass to the exhaust plume? Correct me if I'm wrong but if the thrust to weight ratio of this coolant/thrust system is higher than 1 then it allows for an improvement in the efficiency of the rocket.
It would work, but it would be far from optimal.
Heat recovered from the nozzle would result in steam much colder than combustion chamber temperature (after all, we never allow the nozzle to reach these temperatures, that's what cooling is all about, so the steam wouldn't heat to temperatures higher than the nozzle). That would cool the combustion products, resulting in lower performance. Additionally, we'd need to use extra energy to bring the liquid hydrogen up to temperatures of combustion, which again reduces performance per unit of mass of fuel.
Using hydrogen as coolant we kill two birds with one stone - we keep the nozzle cool, and we heat the hydrogen so it performs better during combustion. The combustion creates far more than enough energy to evaporate all the liquid hydrogen, oxygen, and heat the resulting steam to the desired temperatures, but every little bit helps - the fuel being the coolant returns the energy harvested from the nozzle to the combustion chamber, then releases more, burning. If you used water, it would return the energy from the nozzle, but then it would absorb more from combustion as it's inert, and can't provide more.
Simply put, if you replace water with LH2 as coolant, you're replacing the inert propellant that can't produce any extra energy, just transfer it from place to place, with propellant that not only can transfer the energy from the nozzle but also produce a lot more of it.