No.
The word used in both the Greek and Hebrew has several meanings, including God and his elect such as Judges, Kings, etc.
In John 10 Jesus is not claiming to be GOD, - he has challanged the Priest Judges, saying he is Anointed, Judge, or Magistrate. The Messiah was to bring the end and FINAL JUDGMENT!
When they claim he blasphemes, he quotes from Psalm 82 - Which is a whole section on bad judges, where they are told -
Psalm 82:6 "I said, 'You are (Elohiym), And all of you are the sons of the Most High."
Jesus is saying (as per the OT quote) He is a/or
THE Anointed Judge/Magistrate = Messiah.
Joh 10:24 Then came the Jews round about him, and said unto him, How long dost thou make us to doubt?
If thou be the Christos/Messiah, tell us plainly.
Joh 10:25 Jesus answered them, I told you, and ye believed not: the works that I do in my Father's name, they bear witness of me.
Joh 10:34 Jesus answered them: Is it not written in your law: I said, you are theos?
Joh 10:35 If he called them theos/elect/sons of God, unto whom the word of God came, and the scripture cannot be broken;
Joh 10:36 Say ye of him,
whom the Father hath sanctified, and sent into the world, Thou blasphemest;
because I said, I am the Son of God?
Both Elohiym in the Hebrew and theos in the greek have the meaning - elect - Judge/Magistrate - son of God, as well as God.
*