Yes, just add a copy of your Mobi file to the ~/Documents/My Kindle Content folder or wherever your version of K4Mac stores its files, or drag and drop it to either the open app window or its Dock icon (I forget which, exactly).
Incidentally, there have been reports in the Sigil and Calibre forums that Calibre mobi conversions don't create enough space in a certain portion of the metadata to allow for the extra layer of DRM that the Kindle for Apps use, so it can't be used to convert a commercially-submittable Mobi file.
Though this point may be moot if your client is willing to go DRM-free.
Anyway, the
Kindle Previewer app will allow them to see how it will actually look on several devices.
Hope this helps, and welcome to MobileRead!