Interesting project. The diff that you are proposing to use is a normal friction-clutch type. If it works the way I think it does, the two outputs are locked together until there is a prevailing torque difference that exceeds what the friction clutch can transmit.
I have a funny feeling - nothing more, because I have no experience with it! - that in a roadracing-type application, this probably isn't going to be a good thing. If you are rounding a bend at neutral throttle, whichever end wants to be going faster (due to different effective radius around the bend) will be trying to drag along the other end that wants to be going slower, front fighting the rear, unnecessarily using up "traction circle" lateral grip at both ends. If you had an ordinary open diff, or even a torsen type, it would simply allow the speed difference to happen, without using up grip by trying to fight it. If you had a viscous coupling, the speed difference wouldn't be enough for it to matter. If you had a Haldex, it would probably be uncoupled. If you had an electronically-controllable clutch around the diff (e.g. BMW X-drive), it would probably be uncoupled and acting like an open diff.
If it's a drag-racing situation, it will probably work fine, because using up lateral grip doesn't matter. If you are trying to extricate the vehicle from a snow-bank or ditch or beach sand, it will be fine. For that matter, if it is more of a rally-car situation, on loose surfaces, it will probably be fine.