Depends on how you define "original sin."
To me, original sin simply means that we have inherited the same weaknesses that led to Adam and Eve's first sin, and that those weaknesses cause us to sin as well. However, I believe that total depravity can only be supported by taking Scripture out of context and using a very literal interpretation. Many who believe this theory will point to Jeremiah 17:9 ("The heart is deceitful above all things and desperately wicked"), but I don't think that people sin because their hearts are wicked; rather, their hearts are wicked because they sin. When Genesis 8:21 says that "everything they think or imagine is bent toward evil from childhood," it is referring to the people that God destroyed in the flood, not necessarily humanity for all time (see Genesis 6:5). And when David says that he was conceived and born in sin, he is using a poetic device.
That being said, the Bible does say that we are all sinners, and it clearly suggests that there is an age of accountability. The belief in baptizing babies and small children is based on the concepts of original sin and total depravity, but they are not held accountable for any sins they commit in their lives until they are old enough to understand and recognize that they have sinned. I guess you could say that that is when someone "falls into sin": when they realize that they are sinners and need God's grace for salvation.
There is quite a large difference between an inherited original sin and total depravity. I agree with your assessment of original sin as an inheritance of the inclination toward sin rather than the guilt of the sin itself. However, the practice of infant baptism was around for about a millenium before the idea of total depravity was developed during the Reformation. The belief in baptizing babies and small children is clearly not based on the concept of total depravity.
The idea of total depravity is a lack of the ability to do anything right without God, whereas with original sin we still have the free will to make decisions, some of which are probably morally right, if nothing else out of sheer dumb luck. But, we still do need God's help to be saved and cannot merit that by our works alone (hence
Pelagianism is heretical). Thus we are baptized in the name of the Father and of the Son and of the Holy Spirit as an external sign of an internal reality of sanctifying grace.
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