Short answer. No.
None of the editors having "Anyone with the link" editor rights can delete the file.
The only person who can delete this file is the owner of the file.
You can see that when changing the sharing permissions of a file to
Anyone with the link can
Edit, the option of changing the settings is greyed out with the message
Settings are disabled for public links
Furthermore, when within the file
Edit menu , the option of moving the file is greyed out as well.
One can only use the
Add a shortcut to Drive.
Even if one later decides to delete this created shortcut from the drive, the original file remains intact.
You can safely, publicly share, any file stored in your Google Drive using "Anyone with the link" editor rights.
Your publicly shared file will never be deleted by anyone else but you.
Sleep deprived part amended following the accurate comment by doubleunary.
Please do NOT confuse the above with editors added under
Share with people and groups.
They CAN delete the file and even deprive you of your rights as the owner.