Is there any connection with the semichah when a person is about to offer a korban to the semicha of becoming a rabbi?
Perhaps, the sense is that in both rabbinic ordination and korbanot there is a transfer of one's representation to the other. In the case of rabbinic authority, the already ordained rabbi confers his authoritative status to another. Somewhat similarly, the one who brings an offering, as explained/cited by Nachmanides (Leviticus 1:9), uses the offering as a replacement for himself:
ויותר ראוי לשמוע הטעם שאומרים בהם כי בעבור שמעשי בני אדם נגמרים במחשבה ובדבור ובמעשה צוה השם כי כאשר יחטא יביא קרבן יסמוך ידיו עליו כנגד המעשה ויתודה בפיו כנגד הדבור וישרוף באש הקרב והכליות שהם כלי המחשבה והתאוה והכרעים כנגד ידיו ורגליו של אדם העושים כל מלאכתו ויזרוק הדם על המזבח כנגד דמו בנפשו כדי שיחשוב אדם בעשותו כל אלה כי חטא לאלהיו בגופו ובנפשו וראוי לו שישפך דמו וישרף גופו לולא חסד הבורא שלקח ממנו תמורה וכפר הקרבן הזה שיהא דמו תחת דמו נפש תחת נפש וראשי אברי הקרבן כנגד ראשי אבריו
It is far more fitting to accept the reason for the offerings which scholars say, namely that since man’s deeds are accomplished through thought, speech and action, therefore G-d commanded that when man sins and brings an offering, he should lay his hands upon it in contrast to the [evil] deed [committed]. He should confess his sin verbally in contrast to his [evil] speech, and he should burn the inwards and the kidneys [of the offering] in fire because they are the instruments of thought and desire in the human being. He should burn the legs [of the offering] since they correspond to the hands and feet of a person, which do all his work. He should sprinkle the blood upon the altar, which is analogous to the blood in his body. All these acts are performed in order that when they are done, a person should realize that he has sinned against his G-d with his body and his soul, and that “his” blood should really be spilled and “his” body burned, were it not for the loving-kindness of the Creator, Who took from him a substitute and a ransom, namely this offering, so that its blood should be in place of his blood, its life in place of his life, and that the chief limbs of the offering should be in place of the chief parts of his body.