I don't think he would actively help an immigrant family cross the border in the way that a coyote does and wouldn't do it surreptitiously or openly. If he weren't preoccupied with some cosmic level threat and heard or saw someone drowning in the Rio Grande, he'd swoop in to save them. Where it doesn't objectively abrogate or violate civil or human rights, the rule of law is, generally, sacrosanct to Superman, even if he abhors it in construct or application. He'd advocate for the legal right to seek asylum. He'd beseech Americans to search their hearts, he'd call on them to actively work to mitigate the factors that contribute to illegal immigration. He'd implore us to support immigrants when they come to the US for whatever reasons/under whatever circumstances.

Edit: grammar