Somehow I doubt it. Putin isn't QUITE that stupid, he no longer has anything to gain by supporting Syria. It's why China is only paying lip-service to its alliance with PDRK. The only question is one of hubris. Can Vlad swallow his pride and admit that he was wrong on Syria? The most elegant solution is to simply let Turkey annexe the joint, the Ottoman Empire kept the peace there for a millennium. Will Russia stand for that, given the enmity that has existed between the two for as long (the Tsar and the Caliph fought dozens of small wars in the Balkans)?
There has been a war in Syria for years. Your question should have said war WITH Syria, as the Assad regime is the government of the country. I don't believe there will be a war with Syria, and if there is, Putin will find an excuse to wriggle out. He likes to talk tough, but I doubt if he is dumb enough to risk a war with the West over it.