If you think that the Iraq invasion had anything to do with terrorism...
Personally, I think it was more to do with Iraq's attempt in 2002 to persuade OPEC to switch oil exchanges from the US Dollar to the Euro. Such a move would have seriously damaged the US economy, and the Iraq invasion, IMHO, set out a definite signal to the unfriendly oil-producing regimes the world over that that would not be tolerated.
Invading Syria, (not an OPEC member), would not have sent that signal to Iraq, (or Iran, or Venezuela...), instead, once the occupation got bogged down it would have only emboldened the anti-American voice within OPEC.
In addition, we would see an earlier, and more violent, rise of Hezbollah in the Lebanon. Israel would have to do something... the wider Near Eastern War could turn out to be much more violent than OTL Iraq.