No. Each media item can only belong to one folder at a time.
How It Works
When you move a file into a folder, any previous folder assignment is removed and the new one is applied. There’s no way to assign a single file to multiple folders simultaneously. It’s a one-to-one relationship.
This keeps things simple and predictable. You always know exactly where a file lives. There’s no confusion about which folder is the “real” one or what happens if you delete one of several folder assignments.
What If I Need the Same File in Two Places?
If you need to reference the same image in different contexts, you don’t need it in multiple folders. WordPress already lets you insert the same media file into as many posts, pages, and templates as you want, regardless of which folder it’s in. Folders are for organization, not for controlling where a file can be used.
Pick the folder that makes the most sense for your workflow (by project, by client, by content type) and put the file there. You can still use it everywhere.
Finding Files Quickly
If your concern is finding a file fast, use the search feature instead of duplicating folder assignments. You can search by title, filename, alt text, description, caption, and even folder name. That’s usually faster than browsing through multiple folders anyway.