In theory, but we're assuming his kidneys function, so they should prevent him from being dehydrated by the salt and sugar in sprite. 90% of all soda is water anyway.
Also, I'm guessing alyx isn't eating much, so consuming strictly water would do him more harm than good, seeing as he can become over hydrated. Personally, i'm drinking applejuice and soup, but sprite will still keep you alive for a week.