No, disposable wipes, rags, clothing articles, and paper towels should not be flushed because these combine with fats, oils, greases, and other debris to cause major clogs within the wastewater collection system and treatment facilities. The fibers contained within most “flush-able” wipes are not biodegradable. Also, if your house has a low-pressure grinder pump, the pump may become damaged and the property owner could be responsible for the costs of repair. Please see the Grinder Pump Informational Brochure (PDF) which discusses the use and maintenance of grinder pump systems.
A briefing regarding legislation in the District of Columbia regarding flushable wipes provides additional insights into the issue.