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A literal ton wouldn't do anything measurable but yeah, adding more material of lower atomic numbers would in theory work considering it's a fusion engine and wouldn't exactly scoff at having to break the water molecule before using it.
Edit: like maybe if there was a star with a bunch of particularly wet planets around it and you somehow deorbited them, since as far as I'm aware the elements heavier than iron are just dead weight, they wouldn't put out the star or anything.
I mean, if you add enough iron I believe it would eventually disrupt fusion, but you'd need an incredible amount, far more than you'd ever get from orbiting planets.
As I understand it, the problem isn't the presence of iron, but rather when it starts fusing silicon into iron, as that particular process consumes more energy than it releases, thus eating away at the radiation pressure that keeps the star "held up."
I was thinking that the added inert mass would decrease the likelihood of individual fusion reactions as well as eventually overpower the radiation pressure due to its effect on total gravitational force, but honestly I don't really know what I'm talking about so I could be completely wrong.
Fusing silicon into iron should still release more energy than it takes, fusing iron-56 or heavier should be the point of not gaining energy.