We know that the Arquillians tasked the MIB with finding the Galaxy, giving them "one standard galactic week" (an hour) to find it, before destroying Earth to prevent it from falling into the bug's hands.
We can presume time was still left on the clock by the time the MIB retrieve the Galaxy. Yet, had the MIB not interfered, the bug would have escaped with it on his stolen ship within the hour time limit.
Surely the bug having the Galaxy would have been bad for everybody anyway, but I'm curious, if the bug escaped Earth before the hour was up, wouldn't the Arquillians have sent their battle cruiser after him rather than destroying the Earth anyway? Is there anything in supporting media that would explain what would have happened?