Just wanted to back this up a little bit. This is exactly what happened to me on my last job search. I'm currently in between jobs, starting the new gig after the 4th of July holiday. The company that I went with: I had a 30 minute call with an engineering VP and the hiring manager that was followed by an hour long panel with a few members of the team that I'm joining. I also learned after I had accepted the offer that the person who referred me internally spent about 45 minutes chatting with the same engineering VP about me specifically before they reached out. This was for a staff/lead position and I've got over 15 years in the industry.
I specifically sought out referrals from former colleagues and friends where the interview process put a lot of emphasis and weight on the internal referral and it worked out really well for me. I really hope that this is a sign of things to come, not just for myself and my future employment but for others, at least at the ("actual") senior level.
edit/ Added some more context...