YouGov finds little reason to believe so:
More opponents of the regime strongly disapprove of a U.S. military strike than favor it. 81 percent of government supporters, as well as 56 percent of those who prefer not to say. There’s little evidence that ordinary Syrians favor an attack.
In fact, distrust of America is nearly unanimous among Syrian poll-takers. Only 7 percent of those interviewed thought that the U.S. government was “a friend of the Syrian people.” There wasn’t much disagreement on this point among supporters and opponents of Assad. 79 percent of supporters, 61 percent of opponents and 57 percent of non-aligned said the U.S. was “an enemy of the Syrian people.”