How so? She'd get to meet everybody, and would provide vital information on what injuries O'Brien last collected while kayaking, what Bashir ate, and what Kira and Odo argued about - information without which Founders could not assume the shape of O'Brien, Bashir, Kira or Odo.
Yup, I'm convinced she transmitted the "disease". But she need not have been a Founder in order to do that. (Indeed, had she been a Founder, she would supposedly have been at risk herself, too!) I rather doubt she even knew what role she played in the games of the Founders; contaminating her with the "disease" could be done quite covertly and without her noticing.