yes you can do this, however notice: this is wasteful as you have to run pump and heat from steam condensing is not recovered. You can heat up incoming water with condensing steam - this is called vapour recompression distillation. alternatively you can use heat pump to move heat around
You’re thinking of gases. In condensed phases energy is just stored as a potential energy coming from the fact that molecules are too close to each other (going left of that minimum en.wikipedia.org/wiki/Lennard-Jones_potential). You don’t have gases under such conditions, they condense