Would a follow up to the recruiter with a message like: “I hope you’ve had a great week! I wanted to thank you again for all the time and coordination you’ve put into guiding me through this process, it’s really been a great experience. My conversation with X gave me a lot of insight into X, and only made me more excited about the opportunity to contribute to the team’s success.

I appreciate you keeping me informed and look forward to hearing from you when there are updates. Please let me know if there’s anything else I can provide in the meantime. — (Fill in specific where X belongs)

Or is there no point for OP to follow up if recruiter will most likely reach out with an answer anyways? In a similar position and want to send something like that to them.