Well, only two teams have managed to make up that ground and win the division after being that far behind when April ended. A look (thanks to Elias Sports Bureau):
1987 Detroit Tigers: 10 games back
2006 Minnesota Twins: 9 games back
2003 Minnesota Twins: 8 games back
It's certainly not impossible. And with the additional wild card team, the Angels could make the postseason. But history suggests the odds are long on winning the division for LAA.