I'm not quite sure what "invigilators" are, but I am guessing they are what we in the US call "proctors." In my classes (I have been teaching for 20 years) I allow my pastoral students to take the exams at home. I tell them that if they, as future pastors, cheat on an exam, then they have bigger problems than I can solve.
it depends on the commitment and the personal relationship with God, when my husband was in the course from candidates to the ministry, the professor gives the exam and you goes of the classroom, but before, he told to the students, I qualify his knowledge, but the fidelity measures it God.
Take home exams assume that students have prepared for the exams and that they will consult resources during the exam. That differs from a closed book exam. The time allotted to the take home exam usually does not allow for extensive consultation if the exam is to be completed. Preparation is preeminently important. Proctoring/invigilating an exam is not first and foremost a statement of distrust. You might regard it as a way of signalling that the integrity of the exam is being protected based on the integrity of the invigilator/proctor and the institution represented. The proctor/invigilator guards the terms of the exam and in so doing upholds institutional standards. Her presence also ensures respect for all takers (honest and dishonest) and gives interested parties the confidence that exam and exam results are true and dependable. These are important and long term consequences that safeguard reputations and reliability. It is not foremost about student trustworthiness but it protects it.
The presupposition behind the question is whether trainee pastors are on a spiritually higher level, or whether they could have privileges that other people may not have. What is the spiritual difference or the difference in value between a trainee pastor and another devoted Christian who is not a trainee pastor? For the same token one could ask if pastors in the community might get preferential treatment when engaging in the business market or when they drive on public roads, for example. Are they exempt from certain laws? In my mind, it would not embody the humble, serving spirit of Christ (see Php 2:5-11) to put (trainee) pastors on any kind of spiritual pedestal. Exempting them from exam supervision in distinction from other people would send precisely the wrong message to them. It could in fact make that they perpetuate such a view of themselves later in their congregations and thus elevate themselves above the other church members. All Christians are part of the same body of Christ and all have the same value. There are no exceptions, not even for church leaders; they only have different roles and functions in the body. All Christians, regardless whether you are a leader or an aspiring leader, are subject to the laws of the country or the rules of academic institutions.
We still need humans to supervise the exam. However, the supervisor (invigilators) can give a warning not to cheat but to do his job honestly and responsibly. As the Bible says that whether I exist or not do your duty as a believer. This means that even if not supervised still perform the responsibility in taking the exam.
The aim of supervision is not only to watch against cheating but also to make provision for the basic needs of the students during exams. Besides, pastors are humans and whatever is humanly possible is possible with pastors. Even Judas Iscariot was a pastor.
Some (possibly many) are cheaters. I have taught some, and they have been cheating. If God were to test the pastors through examinations, many would be failures and deserved not the position (the holy divine call of serving God). The point is not just for them being humans, there are people who are not pastors, sinful like others but do not cheat in exams. It is not just a matter of sinful nature (we are all sinful by birth, my Bible Christian belief), but a matter of sincerity, faithfulness and trusting your mind (God-given gift). Cheating pastors in their exams are likely surely to be cheating pastors in their pulpit and pastoral ministries.