Yes, I would agree that Elihu is acting as a mediator in this way. However, I do not conclude that it is God who appoints Elihu to this position. Instead I would assert that Elihu appoints himself as this mediator.
Question: if God Himself is going to show up and appear to Job, why would Job need Elihu? What does Elihu offer that God Himself is not already going to give Job, and much more besides?
Question: if God Himself is going to show up and appear to Job, why would Job need Elihu? What does Elihu offer that God Himself is not already going to give Job, and much more besides?
The two requests of Job are found in Job 9:32-35 Job 9:32 For he is not a man, as I am, that I should answer him, and we should come together in judgment. Job 9:33 Neither is there any daysman betwixt us, that might lay his hand upon us both. Job 9:34 Let him take his rod away from me, and let not his fear terrify me: Job 9:35 Then would I speak, and not fear him; but it is not so with me.
AND
Job 13:19-22 Job 13:19 Who is he that will plead with me? for now, if I hold my tongue, I shall give up the ghost. Job 13:20 Only do not two things unto me: then will I not hide myself from thee. Job 13:21 Withdraw thine hand far from me: and let not thy dread make me afraid. Job 13:22 Then call thou, and I will answer: or let me speak, and answer thou me.
Notice that Job first requests a mediator. Then Job asks God to take his hand away. Then he asks God to not make him afraid. Then if God does this Job says he will speak. (Can you see that these two requests are very similar.)
Then enters Elihu, and he says, Job 33:5 If thou canst answer me, set thy words in order before me, stand up.
In a court of Law this would be the judge ordering the defendant to stand up and make a plea.
Job 33:6 Behold, I am according to thy wish in God's stead: I also am formed out of the clay. (There is no need for God to reaffirm who Elihu is. This is the answer to Job's request and Job understands it.)
Job 33:7 Behold, my terror shall not make thee afraid, neither shall my hand be heavy upon thee. (We should now understand why Job was a young man. A young man would put no fear in Job. Elihu has fulfilled the requests of Job in order for him to make his plea.