If I understand your question, if you look in iOS settings > General > Keyboards, the Auto Correct settings is under the heading of All Keyboards. Based on that, I would say no, a different keyboard wouldn't change the way iOS functions.
Whether I use the stock keyboard or the Google keyboard, the speed spell check is extremely poor. I suspect it is the function of iOS. NOTE: the ”speed” correction was an after the fact correction by the stock keyboard - I am typing on an ASK.
The same Google keyboard on my Android device yields very decent results In direct contrast to the same keyboard on iOS.