Syria joining the Soviets I could maybe see, but why would they attack Turkey? As you said their involvement is probably going to bring in Israel so they would have to worry about their flank on the Golan. Committing their troops on against Turkey is going to leave them vulnerable in the south. They couldn't stop the IDF when it started advancing in 1973, I doubt they can do it in 80s either.
While I like to think of Israel as the good guys, I consider it possible that Israel might not actually attack Syria if Syria attacked Turkey. Israel isn't part of NATO, nor is it officially allied with Turkey. Still, the IDF steamrolled the Syrians the last two times they fought, and this scenario won't have a hostile Egypt in Israel's south. That kind of threat is too much to ignore. What sort of support would the USSR need to promise to Syria to get Syria to act?
I have a different question, though: would it be possible to get the USSR to arm and train Kurds to open up Turkey's flank? The only problem I see here, though, is that Iran, Iraq, and Syria (all friendly-ish with the Soviets) are also holding onto bits of Kurdistan.