Probably not. Russia has a vested interest in keeping Assad in power, so trying to cripple the Syrian regime's air forces, while causing initial disruption, will just cause Russia to ramp up their efforts in the area. Notice it's not "may", it's "will". Russia has been willing to put more skin in the game, so their influence will be felt a lot stronger.
Ultimately, half-hearted military strikes will not topple the Syrian regime. If Trump actually wanted to nullify the regime's air superiority, he would have imposed a no-fly zone. It risks more lives on our side, but it's more effective than trying to destroy every airstrip.
Of course, this then leads the problem with Russia propping up the regime, but Russian influence in the Syrian conflict is not going to disappear with military action. Trump would need to perform some serious diplomatic negotiations to get Putin to back out of the region. Something I highly doubt he's capable of doing, considering they're both stubborn as a mule. Compromise is not in either of their dictionaries.