Yes, apparently for some Canon cameras:
I've done a little bit of research and I have found out that Canon cameras with built-in WiF seem to support something called "Canon Image Gateway" that allows a camera to attach to a WiFi network and send images to Canon's online storage and sharing service. The service can then send images along to other services, including Facebook, Twitter, YouTube, Flickr, Google Drive, and Irsta. The services have to be setup on the user's Canon Image Gateway account, but then can be selected in camera. It appears that this can be made an automatic process, but the process of setting it up may be a little involved, maybe fragile.
The name Canon Image Gateway is a little confusing, as Canon uses the same name for their mobile device software. They also don't seem to have a simple list of compatible cameras, and not 100% of the WiFi cameras support all of the features.
I didn't have time to look at other camera manufacturers, but I know that Nikon either supports "SnapBridge" which works through the user's mobile device or -- when using some of the WiFi adaptors -- FTP connections.
It would be interesting to heard about similar options for other camera brands.