Is it permissible to intercede for his classmate who cheated in the exam and was banned from that course?

Firstly: 

Cheating in exams is haraam, like any other kind of cheating. 

The Standing Committee for Issuing Fatwas was asked: What is the ruling on students cheating in tests at school? 

They replied: The hadeeth “The one who cheats us is not one of us” is saheeh, and it is general in meaning; it includes cheating in buying and selling, in giving advice, in contracts and covenants, in matters of trust, and in exams in schools and colleges and the like, whether that involves plagiarism, copying from another student, whispering answers to them or writing answers and passing them to them. End quote from Fataawa al-Lajnah al-Daa’imah (12/200). 

Secondly: 

It is prescribed to punish and discipline the one who cheats as the university sees fit, such as banning him from completing the exam or banning him from that subject, so as to close the door to this haraam action which leads to weakness, backwardness, promotion of those who do not deserve to be promoted and appointment of people to positions for which they are not qualified. The least that the student who cheats in his tests deserves is to be be failed and banned from the subject in which he cheated. How can he be given a grade that he does not deserve, and how can he advance ahead of other students, when he deserves to fail? 

Based on this, you should not intercede with the teacher for this student. Perhaps he will benefit from this punishment and will not do such a thing again, and perhaps others will benefit too. But if this student did not cheat at all, rather he merely tried to cheat, and that is not his usual habit, and he has shown signs of regret and has resolved not to do such a thing again in the future, then there is nothing wrong with you interceding with the teacher so that the punishment may be waived. 

Thirdly: 

The fact that this student is not a Muslim does not mean that you cannot intercede for him in principle. It is proven that Umm Haani’ bint Abi Taalib put a kaafir man under her protection on the day of the Conquest of Makkah, so that he would not be killed, and the Prophet (peace and blessings of Allaah be upon him) said to her: “We grant protection to the one to whom you granted protection, O Umm Haani’.” Narrated by al-Bukhaari (3171) and Muslim (336). 

This was intercession on her part for that kaafir man, so that he would not be killed, and the Prophet (peace and blessings of Allaah be upon him) approved of it. Similarly, ‘Uthmaan ibn ‘Affaan granted protection to a man who had apostatized, then he came repenting and turning back to Islam, and the Messenger (peace and blessings of Allaah be upon him) granted him protection. Narrated by Abu Dawood (4385), classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

This is something that demonstrates the tolerance of Islam, and the keenness of its followers to seek what is good and beneficial for all people, which will motivate them to think about this true religion and encourage them to enter it. This is the goal that leads the Muslim to treat kaafirs well and uphold ties with them, so that Allaah might open their hearts to Islam and save them from the darkness of kufr and shirk. 

It is clear that this kindness does not mean that one loves them and takes them as close friends, because that is not permissible in the case of a kaafir, as Allaah says (interpretation of the meaning): 

“O you who believe! Take not the Jews and the Christians as Awliyaa’ (friends, protectors, helpers), they are but Awliyaa’ of each other. And if any amongst you takes them (as Awliyaa’), then surely, he is one of them. Verily, Allaah guides not those people who are the Zaalimoon (polytheists and wrongdoers and unjust)”

[al-Maa’idah 5:51] 

“You (O Muhammad) will not find any people who believe in Allaah and the Last Day, making friendship with those who oppose Allaah and His Messenger (Muhammad), even though they were their fathers or their sons or their brothers or their kindred (people). For such He has written Faith in their hearts, and strengthened them with Rooh (proofs, light and true guidance) from Himself. And He will admit them to Gardens (Paradise) under which rivers flow, to dwell therein (forever). Allaah is pleased with them, and they with Him. They are the party of Allaah. Verily, it is the party of Allaah that will be the successful”

[al-Mujaadilah 58:22]

And Allaah knows best.