Does general liability cover water damage caused by faulty plumbing work?

Generally yes for the resulting damage to other people's property, and generally no for the cost of redoing your own work, subject to the policy's terms, exclusions and endorsements.

A standard commercial general liability form pays damages you become legally obligated to pay because of property damage caused by an occurrence — an accident, including continuous or repeated exposure to the same condition. A cross-threaded flex connector that lets go five weeks after you leave and soaks the ceiling below is the classic example. The drywall, flooring, cabinets and contents the water ruined are third-party property damage, and because the work was finished, the claim falls under the policy's products-completed operations coverage. The carrier generally pays the covered damages, less any deductible, and defends you if the customer or their insurer sues.

What the form generally does not pay for is the connector itself and your labor to redo the connection. The "damage to your work" exclusion removes the cost of repairing or replacing your own defective work, and the "damage to property" exclusions remove damage to the particular part of the property you were working on at the time. The policy is not a warranty on your installation.

Close cases turn on the endorsements. Many contractor policies carry a fungi or bacteria exclusion that removes mold remediation, a pollution exclusion that carriers have applied to sewage, and sometimes exclusions for prior work, residential or multi-family work, or uninsured subcontractors. Read those before the first slow leak, not after.