From what I have seen Jay Clayton in an interview said that Bitcoin is identified as not a security so probably when it comes to law making and regulations coming from the SEC we won't see a direct affect to it towards Bitcoin since its not one of their concerns.
The potential intersection I see: Bitcoin exchanges. The vast majority of exchanges support various altcoins and tokens -- that could potentially put them under SEC jurisdiction regardless of Bitcoin's categorization under the law.
My suspicion is that's what Gensler was referring to when he suggested bringing exchanges under national registration and monitoring. He wants them subjected to the Securities Exchange Act and defined as national securities exchanges.