No. If Christ died instead of us, we wouldn't die. The Offering/Offerer is apples and oranges.
Christ was baptized instead/in place of us (and for us), but we still have our baptism in
Christ. Christ's baptism, death, resurrection and ascension become ours because He lived the human life vicariously and for us.
Christ doesn't live human life "vicariously" (i.e., through a vicar). The human life of Christ is the actual, historical life of a man, Jesus of Nazareth, who is born of the Virgin Mary in 1st century Palestine. This man is the Messiah of Israel, and the incarnate Son of God. He lives his own life as a specific human being.
Christ is also not baptized "in our place." I've never heard this anywhere, and I don't know where you're getting this from. We unite ourselves to Christ because he unites Himself to us in his incarnation, death and resurrection, that we may partake of these things, as well. To quote from the Epistle Reading of baptism:
"Brethren, do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? We were buried therefore with him by baptism into death, so that as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life. For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his."
Further, the hymns of Theophany make it clear that Christ's baptism accomplishes the sanctification of the waters. Christ infuses baptism with grace to forgive our sins. I'm reminded of these hymns:
"The River Jordan receded of old by the mantle of Elisha when Elijah ascended into heaven; and
the water was separated to this side and that, the wet element turning into a dry path for Him,
being truly a symbol of Baptism, by which we cross the path of transient age. Christ appeared in
the Jordan to sanctify its waters."(Troparion for the Forefeast of Theophany)
"Why are thy waters troubled, O Jordan, and why turnest thou backward, not proceeding forward
according to thy natural flow? It shall answer, saying, I cannot bear a consuming fire. Therefore,
do I marvel and tremble at Thine exceeding condescension; for I am not accustomed to wash the
Pure; I have not learned to purify the sinless One, but to purify impure vessels. Christ, who
baptized in me, doth teach me to burn the thorns of sins. And John, the voice of the Word, doth
testify with me, crying, Behold the Lamb of God Who beareth the sin of the world. Let us believers
therefore cry unto Him, saying, O God that hath appeared for our salvation, glory to Thee."(from the Idiomela for the Sixth Hour, the Royal Hours of Theophany)