Yes they work. But like everything else in BB, the spec is a gambling. I have a 38y/o player and until the age of 36 he had almost no downs thanks to a lv 6 career coach. After I switched to a lv 4 career coach he had more downs. Today he had his 8th double down and reached 100 TSP.
I cannot find the thread where it was mentioned. It was already 8 or 9 years ago. But if my memory doesn't fail me there was a post by a BB about the career coach. If I recall correct, you have a chance of 25%, that at the training update no negative effect occures --> career spec kicks in. If the 75% happen, your player will receive a decrease of skill(s) (visible or not). But at this point the level of the coach kicks in. Lv 1 will have a higher skill loss than lv4 and this one higher than lv 7.
So a lv 7 career coach won't change the possibility of a drop in skills, but he will reduce the speed of decline.
Unfortunately I cannot find the bookmark... maybe someone else has a link.