If you are asking whether an IUD would remain where it is placed in light of an asana practice then the general answer would be “perhaps”, depending on the placement, the body, and the nature of the asana practice in question.
If you are asking a bigger picture question about the health effects of IUD implementation for one on the yogic path I’d respond in the following way.
In Purna Yoga there are four components we teach: asana/pranayama, meditation, nutrition/lifestyle, and applied philosophy. In the realm of nutrition/lifestyle I would suggest to my students that they consider not placing a foreign object in the uterus and allowing it to remain there over time.
A mindful choice can only be made when the student is fully informed and has weighed the possible ramifications. After that, even though I may suggest a different course, the student’s decision is to be respected.