Nope. A swing and a miss.
The word mediator has a specific meaning and comes to us from two words. In Hebrew the word is
יכח and in greek the word is
μεσίτης. The word has a very specific meaning and narrow semantic domain. It involves a legal dispute as the term comes to us from from Hellenistic legal language.
According to BDAG
μεσίτης:
one who mediates betw. two parties to remove a disagreement or reach a common goal, mediator, arbitrator,
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000).
A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 634). Chicago: University of Chicago Press.
It is used six times in the NT
Gal 3:19, Gal 3:20:
Why then the law? It was added because of transgressions, until the offspring should come to whom the promise had been made, and it was put in place through angels by an intermediary.
20 Now an intermediary implies more than one, but God is one.
1 Tim2:5:
For there is one God, and there is one mediator between God and men, the man Christ Jesus,
6 who gave himself as a ransom for all, which is the testimony given at the proper time.
Heb 8:6:
But as it is, Christ has obtained a ministry that is as much more excellent than the old as the covenant he mediates is better, since it is enacted on better promises.
Heb 9:15:
Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant.
Heb 12:23-24:
23 and to the assembly of the firstborn who are enrolled in heaven, and to God, the judge of all, and to the spirits of the righteous made perfect,
24 and to Jesus, the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel.
The Holy Bible: English Standard Version. (2016). Wheaton, IL: Crossway Bibles.
You are broadening the term because you have a tradition you are trying to shoehorn into the text. If I ask my daughter to get a cup of coffee for me while I am working doesn't make her a mediator between me and coffee. Your argument is silly and invalid.
A.