Why would one say "Хочешь воды?" rather than "Хочешь воду?" It seems I should be using the accusative singular in this instance. Does making it plural give it that "some water" connotation rather than simply "water"?
The latter. With substances Genitive can be used insted of Accusative if you want to reference an indeterminate "some" amount of that substance (note that English "some" has other meanings that Genitive here doesn't).