Definitely not:
„The Syrian army is largely made up of Sunni conscripts, while many willing Sunni volunteers in the paramilitary groups that support regular government forces fight alongside foreign Shia militias, like Hezbollah, against a plethora of rebel groups that are all exclusively Sunni Muslim of varying extremes – both local and foreign.“
http://www.middleeasteye.net/columns/syria-why-assad-still-power-544952547

Also:
“There are a lot of senior Sunni officers who are still in the Syrian army and security institutions,”
A militant in Deir al-Zour told me, “Until now, the majority of the Syrian army (around 60%) are Sunni.”
http://www.al-monitor.com/pulse/politics/2013/05/syrian-conflict-failed-sectarian-analysis.html#ixzz2UiWQhTc