Observed in DOSBox versions 0.72 and 0.73.
1680k floppy images don't boot using DOSBox, although they boot fine in standalone machines.
Example IMG files for easy comparison between 1440k and 1680k images: http://odin.fdos.org/odin2005/
Another example (my own 1680k bootable floppy project): http://www.superkeen.com/peacecorpsfiles/FUZOMA12.IMG
1680k floppies are bootable in just about any PC. Even the NT kernel (NT4-Vista), which broke many other non-standard floppy formats, can read and write 1680k disks.
I don't see any documentation saying that this size is or isn't supposed to be supported, so not sure if this is a bug or a feature request.