Suspended grid ceiling with T-channel on the perimeter?
There's no reason you couldn't do what you have planned. Suspended ceilings are a decorative feature, and not a structural one, so you can do whatever you like. I assume you'll cut your interior channel and lay it over the perimeter channel as normal, as opposed to somehow replicating the locking mechanical connection you'd normally have between interior channels.
You're going to have one particular challenge, though, and that's keeping them flat.
L-channel is rigidly mounted to the wall, so the horizontal portion is more or less stuck in position. You can lay interior channel on it and it doesn't move much.
In your case, you'll be suspending the T-channel and it'll have freedom to pendulum away from level. Laying the interior channel on it will have a tendency to tilt it down on the inside flange.
One solution might be to use pop rivets or screws to tie things together more rigidly. You could simply do this through the mating horizontal flanges, or you could strategically cut tabs into the ends of the interior channel so you can rivet in a hidden fashion:
TOP (PLAN) VIEW
__________________________________________

             rivet locations              &lt;-- perimeter channel
_____________*______*_____________________
            ----..----   &lt;-- tabs cut from center rib of interior channel
         |      ||      |
_________|      ||      |_________________
         |      ||      |

if you are going to rivet from the bottom you might consider just floating L channel, though. It'll look a little more standard since it's narrower and it's usually cheaper.