Now that apparently lab caches has been included in the profile stats (including, apparently, BagdeGen), I think it appropriate to bring up this old topic:
It would seem that a lab cache hide does not appear. Not in the "Hides" tab, not in BadgeGen.
There is no precedence on how to handle hides on geocaching.com since they don't include hide stats at all.
Any plans to bring lab cache hides into the ProfileStats module as well ?
EDIT: They are included in the overall hide count, as evidenced by