Yes you can do this. The JPEG format makes provision for exchangeable image file format
- Color space definition
- Component sub-sampling registration
- Pixel aspect ratio definition
JPEG/Exif is the most common for photography and JPEG/JFIF is the most commonly used for storage.
When the others state JPEG format doesn’t provide for an alpha channel all they are really saying is that there is no widely used formats for JPEG encoding that include an alpha channel.
Have a look at On adding alpha channels to JPEG images, where the author describes and provides a solution to exactly what you are trying to do and uses the the canvas element to render on a browser.