Exactly once, some 25 years ago, Amtrak used an unusual set of electrified track.
In 1978 I believe it was, a freight derailed on the NEC in Metuchen and blocked all four tracks. Thankfully no passenger trains were involved, though did hear that two had a narrow escape. But in any case the NEC was impassable, for several hours while the wreck was being cleaned up, Amtrak trains went from the NEC to the North Jersey Coast Line of NJ Transit (New York and Long Branch, I think) until South Amboy. From there, Amtrak took some rare mileage: Conrail's Amboy Secondary south, through Browns yard, to Jamesburg. From there the trains headed west on the Dayton Branch to re-join the NEC at Monmouth Junction. (see
http://www.geocities.com/transit383/asmap.jpg for an excellent map) I heard that those were the first passenger trains to roll through Jamesburg in decades.
Was that Amtrak route electrified? You bet! The NJCL was electrified at least as far as S. Amboy, and the two Secondaries still had full catenary; the AEM-7's could run just fine. Those catenary wires have since been removed by Conrail, though the towers remain for any future use by NJ Transit. In fact, both routes are contenders for the proposed "M-O-M" (Monmouth-Ocean-Middlesex counties) route, but I doubt they will electrify them. Meanwhile, the NJCL was electrified to Matawan, then to Long Branch since then.
Another electrified line that Amtrak once used -- SEPTA in fact: the branch to Philadelphia International Airport, when direct trains were run between there and Atlantic City in some airline promotion. The locos, of course, were diesel, since the AC line is not electrified, even though some catenary structures near where the line crosses the Delaware River suggest that part of it may have once been. And correct me if I'm wrong, but I think the AC-bound trains parallel, but do not use, the third-rail electrified PATCO tracks.