I'm not sure I totally understand what you're wanting here.
Create a Scrum board which includes all the projects that you're interested in. You will need to be a project Admin of every project. Create a sprint in this board, which can then include tickets from any project.
I think that the sprints will also show in the other boards, but could be a nightmare because people won't have permissions to view all tickets.
Hope this helps
Sprint itself is global entity so it is available for everyone to add it to their issue. However there will be difficulties if issues from different project added to the sprint and you do not have permission for that project, it wont allow you to create/complete sprint.
More confusing thing is board will only throw error but won't show up all issues since you do not have permission to see those issues as mentioned in the earlier comment.
Hence it is recommended to use unique sprint name so people from other projects shouldn't add your sprint into their issues by mistake.
So it would really be nightmare if all administrators do not have permissions to all projects. Not recommended.
Yes as mentioned in the a previous comment, If you add a board which includes all the projects that you're interested in. Assuming you are the admin, should be able to create a sprint in this board, which can then include anything including backlog items from the included project.
Best of the luck