Absolutely!
There are no restrictions, or limitations with regard to image type, or image format, however, some formats are absolutely easier to use than others.
Image files in a vector format are the simplest format to use for customization.
If you are uploading a graphic file with an .ai file extension, be sure that the file has been saved as a ".pdf compatible image file", or it will not upload.
If a bitmap image is all you have, and graphic development services are not what you are looking for, then high resolution .png bitmap images with a transparent background are simpler than .pngs with a background, or .jpgs.
That is not to say that bitmaps with a background can't be used, there will just be a few additional steps through the customizer to set the graphic up to be compatible in a laser engraving application.