Possibly, although if you are doing a sane activity (as opposed to, say, pro football or boxing) injuries are generally a signal that you're not doing it right. E.g. shoulder injuries from downward dog caused by using the shoulders incorrectly and taking the weight there rather than passing it through; moving in such a way as to create a shearing force across the knee instead of using it as a hinge as God intended; or trying to do internal exercises with a bunch of tension instead of using them to root out and release tension.
I think that's the rub. Injuries come from catastrophic, unexpected / unintended events, such as landing an otherwise perfect breakfall on top of a fellow student who happened to occupy your space a split second before you arrived there, or any of a number of zigs that should have been zags when practicing randori at or near full-speed. There are numerous opportunities for this in Aikido, and I don't think the shift towards internals in our art will change this much, unless we stop free style and multiple attacker practice. On the upside there will always be LESS chance for this than in football, boxing, or any non-cooperative, "live" discipline.
And injuries can also arise due to patterns of incorrect movement. But this is because correct movement is hard. Your body tries to tell you that you are doing something wrong, but it is not always clear how to fix it. Not every teacher is a physical therapist or osteopath, and every body is unique. In fact, I would go so far as to say that this type of injury - an incremental thing caused by inappropriate body mechanics - is something that every person practicing Aikido will experience to some degree.
So I wouldn't worry about the breakfalls just because some folks blame bad backs on them. I also wouldn't worry about suwariwaza because some folks blame shot knees on it. I'd worry about whether or not the student takes the time to warm up, stretch, and listen to their body tell them whether they are doing something right or wrong.