Not immediately, but it would be possible to do it as long as you can come up with a reasonable definition of a "bond". Bonds are not physical, it's something chemists like to use as a way to characterize the interactions between atoms. Sometimes they are mainly used for nice pictures, and sometimes they are crucial for computations since specific models, e.g. force fields, contain bond-specific parameters.
But under any circumstance the bond is a fictitious object, and what you mean by two atoms being bonded or not becomes a matter of definition.
In ATK you can compute the bond overlap population between two atoms; see
http://quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/ref.mullikenpopulation.html and search for "bond". If you can figure out a way to use that number to determine the bonding table, and very importantly the bond order, then this may be enough. Writing the output file is the easy part
Another way, which is just based on the overlaps of covalent radii, is also possible. It may be useful for converting files to specific formats, but one should note that the definition of bonds in this case is much more uncertain - which not least would be reflected in the fact that one could not assign any bond order to the pairs of atoms a priori. This method is not officially supported, in the sense that the API may change in the future, so it may not work in some newer version of ATK, but I could provide an example that works in 13.8 at least. The bonds printed if you don't change anything will be those that are used in VNL for visualizing the molecules, since the fuzz-factor (the extension of the covalent radii) is set to 1.1 which is what VNL uses.
Now, there is an added complication due to periodicity, since most file formats that I know which contain bonding information are for molecules. So the example attached is for a molecule (tetralin, to be specific).
