Deoxycholate does not solubilize inclusion bodies. It is therefore often used for washing steps and/or in the lysis buffer when preparing inclusion bodies from E. coli.
See, for example: http://shodhganga.inflibnet.ac.in:8080/jspui/bitstream/10603/29824/9/09_chapter%203.pdf
As detergents are notoriously hard to get rid of, and might cause problems in column chromatography, you might be better off using non-detergents for solubilization, like urea/GHCl (denaturing approach), or even arginine (which is capable of solubilizing protein from inclusion bodies in native form). You would then need to separate the correctly folded population from misfolded isoforms.
As Peter comments, DOC does not solubilize proteins in inclusion bodies (IB) very well but it does help remove membrane related materials and is useful to help wash the inclusion bodies as many investigators have done, again as mentioned by Peter. The IB will become "softer" in the case of refractile IB and the IB pellet may nearly disappear in cases of poor expression levels or small IB or grey IB under phase contrast microscopy. If you need to solubilize and fold the IB then traces of DOC after water washes of a DOC treatment can slow or prevent proper folding or dimerization if that is also required. Some proteins are not affected in folding by DOC, some smaller molec wt proteins with cysteines for example. If you take the DOC route and get correct protein then be sure you prove DOC clearance in subsequent purification steps.