There are examples in core where we have put form elements in a modal dialog, but the form elements are not contained in an actual form.
It doesn't matter if the action is performed by ajax or not - form elements are required to be associated with a form and this will affect screen reader behaviour.
MDL-64331 because we close a modal if you click outside it and the modal does not contain a form. The reasoning for this is that if you are filling out a form, you might lose data if the modal is closed with no warning, but if there is no form it is a better experience to just dismiss the modal window.
Listing 3.6 here because
MDL-64331 will be added to that version.