Your story is nonfactual. The first US airstrikes in Syria were in 2014[1], the first US airstrikes against the Syria Government were in 2017[2]. Both long after the Syrian Armed forces had lost control of the situation.

The mass defection of Syrian Army soldiers and officers to the Free Syrian Army guaranteed that the conflict was going to a bloody mess with arms falling into hands of all parties, long before the US started supplying arms. And no, you can't for certain say that Iraq would have fared better, as Iran would have fueled Shia sectarianism all the same in Iraq as it did post US invasion. Iran in fact was Sadam's greatest concern before his WMD bluff backfired.

[1]: https://en.wikipedia.org/wiki/American-led_intervention_in_t... [2] https://en.wikipedia.org/wiki/List_of_United_States_attacks_...