Schiff's letter is the most childish tantrum I've seen outside of Twittler's account. "If you don't do what we want, I'm going to impeach the president, you doody-head!"
But as a senator, he also has lots of immunity when Congress is in session (which it eternally is these days).
Depends on the charges, but a lot of them that might be filed, he could justifiably claim immunity under the same logic that the Trump investigation was largely bull####: it criminalizes policy disagreement.