Does anyone know if it's possible to allow for pasting of images into tickets in the service desk module?
No, it's not possible. You can create a feature request, but the chances it will be implemented will be close to zero I guess
Assuming you want to change the responses that are automatically sent via email from the procedures for Service Desk -
Yes, it actually IS possible, but it's not easy ... We did it years ago, it involves exporting the current response files to an HTML file and then editing that file and re-importing.
As for adding an image directly into the ticket, that can also be done using the built-in editor to attach the image.