Not directly, though you can use some kind of hidden features to make this happen.
First, should you have the cover already as a separate file, you can select the file where you want to have this cover art and drag and drop the image file from your file manager to the cover art box. In Picard 2.5 and later you can also right click the cover art box and select “choose local file…”.
If you don’t have the cover as a separate file you can use a kind of hidden trick to save it as a file. Select the file where you want the cover from and click on “Show more details” below the cover art box. In the dialog double click on the image. The image should now open in your system’s default image viewer, where you can then save it as a file. Proceed as described above to add the file as cover to the other tracks.
We actually should make all of this explicitly available in the UI somewhere. I want to have the UI around cover art handling improved anyway. In the next Picard release, version 2.5.2, you will also be able to select multiple files and add cover art to all of them at once. In the current version you need to do it per file.