I think such a trail is unnecessary. The Jones Falls Trail is very close and parallels the route. It would essentially be superflous at least throughout the City. Add to fact that certain parts would need to be graded and properly lit. Then the necessity for some form of security or police presence along that stretch while are resources are already stretched. Then the increased likelyhood of jaywalking the rails and collisions. The City can't even afford to maintain (or built) its parks facilities in the first place. So simply because something can be done, doesn't necessarily lend itself to a good idea. Each scenario is different. (Not to mention that the right-of-way doesn't really exist along enough parts to connect it properly.)

Let me backpedal a bit, now that realize you were referring to the southern section. So the first point doesn't apply, naturally, but the latter points are still mostly relevant.

Unfortunately, the part of the Purple Line that is proposed for the Georgetown Branch of the Capital Crescent Trail will be too wide to accommodate the trail (viz. tthe plan to run the trail above the trains in the tunnel that goes under Wisconsin Avenue--under the Air Rights building). The rail line also necessitates cutting down hundreds of trees to accommodate the overhead catenary lines, which would eliminate any shade along the trail abutting Town of Chevy Chase and several other towns. It would effectively destroy that part of the trail.

Trees must be removed for construction of the Purple Line, but that does not equate to permanent loss of all shade on all parts of the corridor. Small trees can quickly be established near the trail to provide shade without interfering with overhead catenery lines - there are numerous places around the world where this is done. See http://www.purplelinenow.com/rail_trail_is_green.html for examples.