Herod was an Edomite. So, being an Edomite, he was a false king sitting on the throne at the time of Christ’s first coming. Do you think that fits as a type?
This text is from a transcript of a talk by David Gooding, entitled ‘The Salvation of the Lord’ (2001).
When you say in type, or in prototype, yes, I think it is significant that Herod was an Edomite. He is often referred to as the 'King of the Jews', but he wasn't a Jew himself; he was an Edomite. And the Genesis record is that there were kings in Edom before there were kings in Israel. We recall the first story about Esau and how he got the name 'Edom'. Although he had the birth right, so to speak, he sold it for a bowl of stew (Genesis 25:29–34). He preferred to have a full stomach now, rather than live on promises for the future.
Herod showed similar propensities. He was determined to be king now, and so when our Lord was born of the seed of David with a claim, therefore, to being the true king of the Jews, for Herod this was a political claim, and he determined to wipe out any such claimant that might compete with him. He wanted to be king now. So, yes, you may think of Edom in that connection.