I don't think there will be many treasures left after the Syrian civil war, but the government likely already has some either out of the country or somewhere safe. Many countries lost countless treasures during World War II, but also saved many in this same way. I think the Syrian govt. will take the same steps so there is some of their heritage left.
It's tough to think anything will survive the Syrian civil war, let alone these ancient treasures. When human life has so little value in this conflict, certainly neither side is making a big effort to preserve archaeological relics from the ancient past. The loss of historical artifacts is sad, but not as sad as the loss of life.
The mass destruction of Syria and its ancient treasures will be all destroyed by terrorist as a demonstration of their control and lack of respect for other cultures. It is a loss for all societies to witness this cost of civil war but there is little to stop the destruction. The ancient treasures are a symbol of civilization and education that conflicts with the terrorist groups.
At the rate treasures are being destroyed in Syria it is highly unlikly that any ancient trearsures will be left at the end of the Syrian civil war. In fact, the level of hostilty and the amount of destrution going on suggest that the Syrian Civil War will not end until there is nothing left in the country at all.