Georeferencer does not support transparency on uploaded maps at this moment - it is a feature for one of the future releases.
In the meanwhile, there is a workaround - if you have the data to process feel free to use our MapTiler (
https://www.maptiler.com/) which does contain a comfortable interface for visual georeferencing similar to Georeferencer - and it does support transparency out of the box (for data supplied with alpha channel such as transparent PNG or for data where a single color should be turned into transparent).
Hosting of produced maps is possible directly on any web server or even Amazon S3.
Regards,
Petr