Do you think Terri had the right to try to swallow her own food and water if she chose to do so? Yes or no.
This is something of a strawman argument, don't you think? Since Mrs. Schiavo could not safely swallow enough food/water to sustain her, and lacked the cognitive ability required to "[choose] to do so", your question is, at best, hypothetical. But if she had been undoubtedly capable of a) volition; and b) safe oral nutrition and hydration, (that capability being determined by reputable medical personnel), then certainly she would have had a "right" to eat and drink orally. I don't believe anyone would say otherwise.