It wouldn't be doused if that's the question. Its not a fire in the normal sense, its a nuclear reaction. This is more like asking if a nuclear bomb can detonate underwater.
The water would be steam long before it hit the star, but that vapor would get sucked in. Then, I see 2 things happening based on adding raw material to the star.
1, the added hydrogen would fuel the suns reaction. I think. Im not sure if the sun, given infinate material, would grow or if it would simply take longer to exhaust its fuel. With all that fusion going on, and an influx of material, its probably destined to be a black hole assuming infinate water.
2, maybe that hydrogen is not useable in water form, or maybe the oxygen gums up the stars reaction, and the star burns out. I believe It would become a brown dwarf in this case.
Look up stars Main Sequence for ideas on this, how they evolve based on the materials they contain. But for a nifty, reality ignoring science fantasy approach, you could say that the star slowly grows (or rapidly by star standards). And threatens to become a black hole at any moment. Just remember that functionally, water on a star wouldn't dose anything. What your really doing is adding material to the reaction.