Only if it's the 1940s, early 1950s, or earlier, and neither effective photovoltaics nor space nuclear reactors have been invented yet.
The question includes some mistaken premises.
First, modern solar cells get better efficiency than that. Commercial solar cells may have efficiencies in the mid to high 20s, and spaceflight obviously uses the best and most efficient flight-tested photovoltaics available.
Second, "efficiency" is usually not the most relevant consideration. For power in space, what is important is often output power per weight, or lifetime energy per weight (if considering things like fuel cells, gas turbines, or nuclear reactors where the amount of fuel is finite). Other extremely important things in space applications include simplicity/reliability (moving parts are typically to be avoided), and ability to be miniaturized (not that great for steam engines).
Third, efficient steam engines do not work at the boiling point of water. Instead, water in boilers is pressurized so that it boils only at a much higher pressure, and steam is superheated to 500 deg C or more.
Forth, steam engines are heat engines, which are fundamentally based on their ability to release heat, at a low temperature. This is easy to do on the Earth, where you can have air-cooled or water-cooled condensers. For a spacecraft, it can only be radiated, and radiating large amounts of power requires large, high temperature radiators. This makes heat engines in general prolematic in space.
In the 1940s and 1950s, speculative design for spacecraft and space stations often included steam engines that used mercury metal rather than water, but otherwise worked much as you describe. Parabolic mirrors would focus sunlight onto a mercury boiler, and mercury vapor would pass through a turbine and then be condensed into the liquid in condenser-radiators. Mercury was favored because the condensation temperature would be much higher than with water, and therefore radiation would work vastly better.
As the 1950s wore on, it became much more apparent that nuclear reactors would be a far simpler and more practical option, and it was often assumed that all spacecraft would use nuclear power. Meanwhile, it became apparent that space exploration would be done with small capsules and tiny automated satellites, rather than the huge atomic rockets of Heinleinian science-fiction lore and Von-Braunian theorizing. For these applications, solar panels provided a vastly lighter weight (no big heavy turbines and pipes and valves) and more reliable (no moving parts is always a huge benefit) option. For nuclear power, power conversion is likely to use the all-gas Stirling or Brayton cycles rather than steam, or to use no-moving-parts options like thermionic or thermoelectric power.