Your pump idea needs to have a pulsing action.
Heat the water up, generate a steam bubble, push water through the outlet valve.
Then turn the heater off, allow the steam to cool and condense, suck water in through the inlet valve.
Repeat.
This will work at quite a large scale, and I have made a couple of these in the past.
Note: At anything larger than a mm in size, you need to have the outlet valve BELOW the heater, otherwise the steam will go out the outlet valve, and not the water.
As for cavitation, this will depend on what temp you cool the water down to. The cooler the water, the more vacuum it can sustain without cavitation. Room temperature will get you to about 9.8 metres of head.