Would anyone ever have really heavy periods if they use an intrauterine device?

Yes often not always. Many times bleeding gets heavy after iud though not always iud causes at times irritation in endometrium increasing blood flow and more blood loss.
Depends which type. Typically the Mirena (levonorgestrel) will cause lighter periods due to the progestin released by the iud. The paraguard, copper based, can cause slightly heavier menses because of its reaction to the endometrial lining. The Mirena (levonorgestrel) is usually indicated in someone who has heavy cycles that need control.

Related Questions

What are the side effects of the Intrauterine device? And is it a solution for heavy periods and not controlled?

If you use. Mirena (levonorgestrel) it secrete progesterone and after your body gets used to it the heavy bleeding should stop altogether. It might take a few months though. Cramping at first can be a side effect as well as irregular bleeding.