The probable answer is “no.” The Sun involves a special type of fire that is able to “burn” water, and so it will just get hotter, and six times brighter.
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Now, will such a star burn? Yes, but not with the type of proton-proton fusion the Sun uses. A star 1.7 times the mass of the Sun will heat up and burn almost entirely by the CNO fusion cycle, after making some carbon and nitrogen to go along with all the oxygen you’ve started with.
One nit, and a followup question:
Water is 89% oxygen BY MASS. And the Sun’s overall density is 1.4 times that of water. So if you have a volume of water the VOLUME of the Sun, it will have 1/1.4 = 0.71 times the mass of the Sun, and this mass will be .71*.89 = 63% of a solar mass of oxygen and 8% of a solar mass of hydrogen. The Sun itself is 0.74 solar masses of hydrogen and 0.24 solar masses of helium.
The reason the sun is denser than water is the gravitational compression, which would also be present in a bucket of water the size of the sun. So you’d probably have even more water than this. The question is whether or not the water in such a bucket would ignite fusion all by itself. Not enough mass for CNO, it would seem. A third of the atoms are oxygen — would that impede the p-p reaction? That’s about the only question I didn’t see the author address. Very thorough — almost like a What If answer.