Yes and no.
Regulations on mass texts are far more strict than they are with mass emails, and the added data of transferring what could be a large image or video to potentially thousands complicates things further.
That said, there is an easy work around.
First, you'll need to make sure your image or video is hosted somewhere. We prefer Imur and YouTube, as the links are especially short, but Google Drive and DropBox also work great.
Then, you'll want to copy the direct link to that image or video and paste it into the text. Most modern smart phones will read the link and automatically place a preview image in the text.
NOTE: Make sure what you have is a direct link to the content you want to text - not a link to your YouTube channel page or Imgur account. Test it in your browser before sending.