No blade geometry permits that to actually happen in practice...but in theory...
...that would make us call it a "steam compressor" if it did successfully operate. And most likely, it would require custom turbomachinery design that is much differnet than that of a turbine. If you were to make a bi-directional steam turbomachinery device, it probably wouldn't be very energy efficient in either direction, because these devices work better if designed for their specific application.
What must be true though is that the steam must enter a compressor as superheated if it is going to be compressed. Otherwise, if wet steam (two phase fluid) enters, that results in slugging of the compressor. Often times, hot-gas bypass is used as a method, whereby the compressor output gets throttled and mixed with the input stream, to ensure that superheated fluid enters.
This is a common problem to solve for the vapor compression refrigeration cycle, as the vapor compression refrigeration is essentially the reverses of the Rankine cycle (steam power plant) processes, except with a different flavor of fluid than water.
Water WOULD be perfect for a refrigeration (due to its very favorable heat capacities, latent heat, and conductivity), but unfortunately it freezes at zero celsius (and we usually desire to operate the refrigerant colder than that). But, be glad that it does freeze at zero celsius, because otherwise we wouldn't be living and here to discuss it.