I think it is very unlikely that they will integrate their system with yours. But from what I can see it works like this: on a regular schedule, they compute the awards and accolades of all Hubbers and they give it to them. These are the messages that you see in your Hubtivity and profiles.
The accolades themselves only appear every 24 hours when the profile pages are recomputed. So when you receive an accolade it may take up to 24 hours before the image of the accolade is actually shown on your profile (together with other accolades on the right).