I had a look into this recently. You would have thought that there would be a natural connection as there are so many similarities in the types of contracts. The issues I came across were:
* Projects available: relatively few "business/management" projects available on KTP, as opposed to scientific/engineering/techy projects. Does the KTP project content match the kind of consulting that you want to do afterwards?
* Length of projects: two years or so is a substantial chunk of time relative to the scope of the projects. Will you be working at the same pace and to the standards/schedule usually expected of a consultant?
* Prestige of the sponsors: the universities accrediting the projects don't tend to be the names that consultancies look for unfortunately. Will you be able to walk away from the project with something substantial on your CV?
I did a shorter project (couple of months) that was a pilot for KTP at Birmingham. I found that useful experience but I don't know how much more a full-length project would have given me.