bikebus,
Actually, the federal definition comes into play with respect to safety standards only. Low-powered electric bicycles (speed under 20MPH and motor under 750W) have their safety standards set by the Consumer Product Safety Administration rather than the National Highway Transportation Safety Board under the rationale that they're a consumer product, not a "motor vehicle." More powerful electric bicycles must meet the NHTSB's more stringent safety standards set for mopeds and motorcycles.
Congress has left it up to the individual states on how to regulate the operation of electric bicycles on public rights of way, including licensing. With respect to federally-funded pedestrian/bike trails and walkways, Congress issued a prohibition on their use unless a State has authorized such use by "electric bicycles". (See the permanent amendments to Section 217(h) of Title 23 of the United States effective upon enrollment of Public Law 105-178.)
http://www.fhwa.dot.gov/environment/bikeped/sec217.htm