Pictures and diagrams, yes. As ASCII art, which is to say using letters and numbers laid out in such a way as to form a picture, I'm not sure if that ever happened.

There were several different inventions over the history of the telegraph used to transmit images.

The pantelegraph physically scanned a specially prepared plate and sent electrical impulses over the line, where they were translated into images on another special plate. It was a commercial failure due to lack of marketing.

The Bartlane Image Transmitter was a greater commercial success and permitted the transmission of grayscale photographs over the telegraph wire.

Then of course, the old standby of using grid coordinates to send a picture (also, a brief mention of the use of early emoticons here) also was used to an extent.

For the most part though, the telegraphs were not used to transmit images. The technology was clunky, and wire time was expensive. Sending words was faster than sending data, and it was easier to have skilled artists illustrate an account of an event than to attempt to send crude images over the wire.