Bigbnuzz,
I ride the CCT from its Silver Spring end down to G'town everyday and find it a very relaxing ride. My office is over in West End so I have to navigate a few blocks on roads, but not a problem. Depending on where you are in Silver Spring the CCT could take you out of your way. Also if you haven't ridden it the stretch from Stewart Avenue to Jones Mill road is very rough and rutted. There is also another brief rough section just before the Bethesda tunnel. Both strtetches are ridable, but on a skinny tired road bike it might be a hassle.
If you come down Georgia Ave. both R St. and Q St. have bike lanes which might help you get across the city. Since GA Ave. becomes 7th St. from there to G'town is going to be 25 blocks or so (probably 2.5 - 3 mi.) Of course if you like traffic you can come down GA to where it turns into 7th St. and then turn right on RI Ave. which runs right into M St. at Conn. Ave.