Even though the extreme eastern section of the C&O goes through dense suburban and urban areas, I still enjoyed a "rural" experience almost all of the way to DC. It was only within 10 miles of DC that the C&O became crowded. I rode this section the Sunday before Columbus Day and the weather was nearly perfect. If I had pedaled that section on a weekday morning, I doubt I would've had to share this section of trail with many other people. The C&O is shrouded by forest for most of its length so it was only within 5-10 miles of DC that it really felt urban to me. Plus, like others have said, the GAP and C&O's surfaces are mostly crushed limestone, so you shouldn't encounter many people "jogging/skating" away from towns the larger population centers along the trail like Cumberland, Harpers Ferry, and DC. This also applies to the GAP, especially near Pittsburgh.
In general, I abhor cycling through suburban areas, unless I am confident that the route is safe for bicycles. Too often, when riding towards a suburban or urban area, I've ridden semi-quiet rural roads that quickly became busy 2-4 lane highways with limited or no shoulders. I would highly recommend sticking with the C&O Canal all of the way to DC as it will take you nearly all the way to the National Mall without the stress of cycling on unknown suburban or urban streets.
Cdavey warns about the challenging terrain of Appalachians. He is right. The GAP/C&O almost exclusively follow stream and river valleys. It is the easiest route across the Appalachians that I know of. Tunnels along the way eliminate the need to climb any mountains unless you want to. There are plenty of opportunities to leave the GAP or C&O and explore quiet rural areas if you would like. I really enjoyed cycling up to Mount Davis (PA's high point) and exploring Antietam National Battlefield.
The GAP/C&O is a spectacular ride, even if it isn't the most physically challenging route across the Appalachians. I really would love to ride it again.