There are three statuses for offer
Disbled status - Offer is invisible and all the publishers links for disabled offer won't work. So the traffic stops immediately after setting this status.
After the click affiliate will get this message.
Active status means that offer is vosible for everyone and works as usual.
Paused status works as usual "active" offer (All the clicks and conversions are counted by Affise), the difference is that offer is not visible for the publishers.