I speak from a Lutheran perspective. In our confession we say this - AC II.1. 1] Also they teach that since the fall of Adam all men begotten in the natural way are born with sin, that is, without the fear of God, without trust in God, and with 2] concupiscence; and that this disease, or vice of origin, is truly sin, even now condemning and bringing eternal death upon those not born again through Baptism and the Holy Ghost.
In general I think we would object to the terminology of TD. The reason is that it can mean that man is not able to do what is ethically good. We know there are atheists who,from the outside, appear to be ethical so one looking at TD will find TD puzzling. This is not what Original Sin means. What we mean is that when it comes to moving towards God and doing what he commands we are impure and are not able to do what his Laws demand.
Also yes that is correct we would rather talk about Original Sin rather than get to the paradigm and terminology of TD.
LPC