According to the data "Der Spiegel" reported about in this article Why Syria Will Remain a Chemical Weapon Superpower, the answer is no.
According to experts Syria's chemical weapon arsenals would survive and parts of it remain even after a military attack by US Forces. Syria has too many powerful chemical weapons and they are very complicated to destroy.
Below are excerpts of the article (in German) in "Der Spiegel" (my own rough translation):
Several hundred tons of mustard gas, several ten tons of VX and several hundred tons of Sarin gas are in the Syrien arsenal of chemical weapons. That was revealed in a list that the French DGSE and their military spy organization DRM collected over more than 30 years. With a total amount of over 1000 tons the Syria chemical weapon arsenal is one of the biggest in the world. The toxic weapons can be transported with SS-21, Scud-B and Scud-D missiles as far as 500 km radius. This was published today in the Paris "Journal de Dimanche", who have received this declassified list.
Such huge quantities of chemical weapons could only be destroyed with a massive deployment of ground troops. The Pentagon estimates that around 75 000 soldiers and specialists had be send in.
Nobody knows exactly where those weapons are stored. Assad is said to have moved the arsenal around in the last months and spread them out even near to cities.
Even if they knew where the weapons are located, the destruction is almost impossible. If you bombard the depots, huge amounts of toxic gases would be released in the environment, a disaster for civilians and the environment. To annihilate the chemicals you would need temperatures of over 650 degree Celsius (1202 F) said French expert Ralf Trapp.
If the weapons are in bunkers, the Tomahawk missiles are not the best weapons to accomplish the destruction of those chemicals in the bunkers. It would be a challenge, said Amy Smithson from the James Martin Center for Nonproliferation Studies in the "Time" magazine. They would fear toxic clouds generated by the explosions. Everybody who lives near would be in great difficulties.
AP reported that according to sources of US spy organizations it is not known who controls part of the chemical weapons arsenal. Therefore it is theoretically possible that Syrian rebels have seized some of these weapons and used them.
One could bombard the factories who produce the chemical ingredients to produce the chemical weapons, but then what is that good for as Syria has already so many weapons to begin with, said former Pentagon employee Steven Bucci to the LA Times. It won't help he said.
These are not news for those who read all about it before, but I hadn't had the chance yet and though I have read comments here about it, it sinks in earnest only now. The article got negative comments saying that it has "only copied from US source articles" and "that 'Der Spiegel' had not done their own recherche", which actually wouldn't be something new.
But honestly what kind of sense would it make to shoot Tomahawks into Syria under these circumstances? I don't get it.