Only if they intervene to defend the laws they passed.

They can't intervene when someone says they aren't following the laws they passed, because they're the ones getting sued.

Intervening basically just means "the outcome of this suit between two separate parties might damage our party in some way, so we need to intervene to show the court where we stand and why a ruling to one of these parties unjustly might effect our party." At least, that's how lawyers see it.

In reality, it kinda looks like NAACP sued the wrong people over Voter ID laws not because the laws were unconstitutional, but because the Governor didn't have a successful veto of them.

Another way of putting it is this: "We sued the Governor who vetoed the bill like we wanted but it didn't work, so it's his fault."

Of course the House and Senate have a reason to intervene, because it's petty and stupid as hell, even if they don't care much about the Governor.