The Iraqi and Kurdish coalition who took on Islamic State in Mosul did an incredibly good job under very difficult circumstances. The terrorists employed tactics such as using civilians as human shields and attempted to launch several offensives. Despite the brutal nature on the ground, the Iraqi-Kurdish coalition achieved their objectives ahead of schedule.
If you see US news, there's a lot of discussion about how U.S forces have helped to wrest Mosul from ISIS. It seems that the combined coalition forces are "pummeling" ISIS and working alongside Iraqi forces to free Mosul from ISIS. Either way , there's still death and danger for coalition troops. Anything that weakens ISIS is a positive.
No, it is my belief that the offensive by the Coalition forces against Mosul is not a success because it is still relavant today, which, to me, means that the problem has not been solved completely and there is still a threat for people from Mosul forces which can be unsafe.
Assuming that the coalition forces are able to drive ISIS from Mosul, the systemic problem of ISIS will remain. ISIS and fundamentalism is a cancer on the social fabric of the Middle East and destroying one group will not eliminate that problem. Assuming ISIS is driven from Mosul the follows will just scatter or splinter into smaller and less concentrated pockets of fundamentalism. The fight in Mosul may be a geographic success, but planting an Iraqi flag in the heart of Mosul again will not fix the ultimate problem.