No. "Totally depraved" would mean that someone can do nothing good at all, even with help, not just partially good and partially evil. This world does not leave us the choice of "absolutely perfect" or "absolute evil". More correctly, the definition should be "partially depraved", since our motives are very rarely totally evil.
The world is not black and white. There is a lot of grayness in this life, even amongst those who claim to be led by the Spirit of God.
Regards
"Totally" could mean what you say, but that obviously isn't the way it is used by those who believe in it. It describes a current condition which IS changed by the power of God. The point of it is that we cannot come to God on our own. Our separation is total. No matter how smart we are, and no matter how strongly we perceive our inner goodness, we are going to be lost without divine intervention. It is "dead" vs. "wounded". God raises the dead.
More correctly, the definition should be "partially depraved", since our motives are very rarely totally evil.
I think that would be the Catholic position, since you believe we are born with inner goodness that we use to cooperate with God. Total Depravity is meant to distinguish from that.