Canonically, yes, and in committee and investigations. But in modern times the courts tend to interpret it more broadly.
I'd think in this case it's ambiguous, and a decision would come down to venue shopping. But if I were on the bench, knowing what I know right now about his case, I'd probably support immunity, though with considerable regret.
Most likely, though, I think they'll strike a deal where he doesn't seek reelection in return for not being investigated or charged.