Do "water-worlds" not have plate tectonics?
can we say that a water-world does not have plate tectonics?


No we can't. Take for example Earth, add in a lot of water to cover all of the continents and you get a water-world with active plate tectonics. The driver for plate tectonics is not whether water exist or not on the surface, but rather the internal heat a planet contains.

Or, the plates of plate tectonics could actually be water ice, as is hypothesised for Jupiter's moon Europa. You have to remember that currently our sample size is one. There is only one planet where we know for sure that there are active plate tectonics, and that is Earth. Ruling out plate tectonics on other planets just because we don't know how it will look like or how it will work is not correct.

That said, water plays an important role in plate tectonics on Earth. Be it modifying the composition of the crust, changing the strength and ductility of the rocks, or some other process.


  then can we also say that these water-worlds cannot harbor life?


No. Again, our sample size is one. There is only one planet we know with life and that is our Earth. Who knows what may be out there? For starters, we don't even know what fired up life here on Earth in the first place. It could be volcanos or hydrothermal vents in the ocean around hot spots, which are (almost) independent of tectonic activity.

On a personal note, we've all seen how astronomy advanced from "are there any other planets out there?" to actually discovering hundreds of them. What was once the exception is now the rule. Who knows, life might actually exist on just about every solar system out there.