Given an ext4 harddrive (not SSD) with no files, is running
sudo shred -n1 /dev/sda
# one pass, no zeroes, over whole drive
demonstrably less reliable than using Bleachbit's "Wipe free disk space" tool on the same location?
(As far as I can see Bleachbit doesn't run a zero pass. If it does, assume shred -zn1 for comparison.)
No
The wipe free disk space tool will overwrite free blocks. Here you are overwriting the full disk.
While with the wipe free disk space tool there could be remaining data in slack space of used blocks¹ (and perhaps some other blocks that cannot be overwritten), with shred you are overwriting the contents of the whole disk, so it seems that the shred solution would perhaps be more reliable.
Note that you are not defining what you consider reliable, and both solutions will probably be similar, but given that you asked is shred is demonstrably worse, the answer is clearly no.
¹ Ok, they could be overwriting that, too (editing every file file to enlarge with random data, and then shrink back), but it would be an unusual move (and could conflict with other processes, not to mention files the OS won't allow to touch...).
