There is nothing that prevents you from hiding, animating, etc. crucial elements in your page's DOM. These decisions are left up to you. As a note, these elements are still present within the page---unless you explicitly delete them---so you can always restore them need be; for example, hide x until the user does y.
Therefore, it is crucial to think of any consequences of DOM modification when laying out a page's markup. For example, it may require wrapping elements to hide children elements, whilst preserving the dimensions of the parent element, so as not to break the layout.
I hope that this helps.