No, he didn't. Assuming Golem has Sturdy, like they usually do, he would have lived the banded Earthquake like they usually do, at which point there are two options. Either it kills the Dugtrio or it dies the next turn. If Dugtrio dies, its owner will switch into something that can kill Golem from such a small range, maybe even a Jirachi. And Golem either switches or dies. If it switches, Suicune may freely come in and, well, Hydro Pump Jirachi. However, predicting the OBVIOUS water attack, Jirachi will switch out to a Toxicroak to absorb the Hydro Pump. If Golem Dies, Suicune comes in instantly to defeat the Jirachi with a Hydro Pump, but Jirachi can switch into Toxicroak anyway, predicting the, again, VERY obvious Hydro Pump. If Golem doesn't kill Dugtrio, it has to die the next turn (because it can't switch out of Arena Trap), at which point Suicune has to come in to use the Hydro Pump, which is so obvious that we can switch into Politoed to resist it and use the HP Grass on that thing.