Yes, but for it to work on the iPad the user will have to open the form in Readdle's PDF Expert app, which is not free like Adobe Reader.
Creating such a field is as simple as adding a standard button, setting the layout to something other than "Label only", and adding the following Mouse Up JavaScript:
event.target.buttonImportIcon();
When the button is clicked, it will prompt the user to select a file that contains the image, then the image will then be placed as the button's icon.
Acrobat DC had an update that included a new type of field (Image field), the is automatically set up as I described above. Note that Reader (Windows/Mac) can import from PDF, JPEG, TIFF, GIF and BMP. Acrobat can import from anything it is able to convert to PDF, including other image formats.