Since you can get a period and ovulate when using hormonal and non-hormonal IUDs, training with an IUD is quite similar to training with a regularly recurring cycle. This is because there is a much lower dose of progestin in hormonal IUDs compared to pills and other methods, while non-hormonal IUDs release copper.
As a result, ovulation isn't usually prevented with IUDs. Like your menstrual cycle, it's important to track symptoms across phases, and assess the impact it has on your training. Consult your doctor to assess which type of birth control is best for you.