Probably not.
Syria is pretty insignificant when it comes to global politics. If any major global power chose to fight Syria, it would just turn into another Afghanistan or Iraq. The invading force would have to occupy Syria for an extended period of time, and they would likely not gain anything from it. The likely course of action is that Russia and the United States will supply the government and rebels, respectively, with weapons and ammunition. On the other hand, Russia may just cut its losses and try to distance itself from Syria, too. The UN/NATO may even help the rebel forces by conducting air strikes on key military/strategic targets. However, nobody really has anything to gain from directly engaging a nation like Syria in a prolonged war.