Many of us here have taught recruits before; you get fairly good at telling those who are milking it from those who are really sick and need time to get well.
There's a difference between getting recoursed for something like missed training due to illness and getting recoursed because you weren't meeting the standard. No one wants to get recoursed for either reason; moving to a new platoon, new instructors, new recruits, etc but the best advice I can give to him is if he is recoursed, accept it, go to the new platoon and perform. There will be a feeling out time between him and his new coursemates but that should be brief. If the recourse was just for missed training due to strep throat, he'll likely fit in with the new folks in a day or two and within no time at all life will be 'back to normal'.
The staff at the school will make a determination if there is the ability to do what is called 'remedial training' (quite normal) in the time available to them. However, because of so many varying factors, it can often be better for both the recruit and instructional staff to 'recourse' the recruit back even a week or two; this is not a punishment. It is just an administrative training procedure that ensures the recruit gets the same training to the same standard as everyone else. At CFLRS, there are courses in Week 'X' almost every week of the year. Because of this, the best course of action to meet the recruits' training needs (paramount and far more important than a recruit staying on the same platoon) can often be a recourse.
Like everyone else, I was once a recruit and the last thing I wanted to do was the ol 'kit bag drag' (recourse) but it happened 27 years ago when I was in Basic, it happened many time between now and then...if it happens, it will suck for a bit and then life will go on. No one wants to leave their 'new family' during Basic, but it will start a process of learning to adapt to new peers and superiors that will likely be the norm in the first few years in the military anyways. Once he gets his first posting, he will likely spend time in different Squadrons, troops and crews - working with 'new people' will be normal. I am aircrew and I rarely fly with the same 'crew' for very long as people are moving around constantly. Just part of normal life in a crew/troop/Squadron environment (like crewmen work in) and something you get used to really quickly - I was a crewman in a former life. Its a chance to make new friends and all that stuff too.
Good luck to him, tell him to just keep his stick on the ice no matter what team he ends up on.