You used the water and admit as much, so yes, they could make you pay. More realistically, they'll decline to open a new account and continue water service unless the arrearage is paid.
I would have been very surprised if they had a mechanism for you to make payments on a plan that's in somebody else's name, or to somehow transfer that balance over to a new account and allow for payments on it. Absent an existing mechanism, the chances of getting a utilities bureaucracy to fashion a special remedy for a single customer hover between slim and none. (I'm not defending bureaucracies; I'm simply observing how they work.)

