Ben Y. Zhao
Ben Y. Zhao, Professor of Computer Science, UC Santa Barbara.
I would say no, and apply widely to PhD programs next year.
1. While I argue often for students to emphasize individual faculty over departments, that's not the real question here. Here it's an issue of should you skip applying widely to different PhD programs to see your options. I am ALWAYS in favor of maximizing all your options before making a decision. So I would never advocate shortcutting the process, and not even seeing what programs you can get into.
2. I don't know how often people cite in mathematics, but 1500 in 4 years doesn't sound like that much. My ex student had 1000+ by the time he graduated and started his faculty job. Of course journal articles take more time than conference pubs which are the primary venue in CS, so I would expect math citations to be worth more. Still... I expect some of the best academics to be at schools lower in rank, but completely unranked? That's unusual if the faculty member is really good.
3. If this faculty member is actively recruiting, then he/she will be thrilled to have you next year. You're not losing anything by waiting to see all your options.
4. Even if this faculty is amazing, you need good departmental support in logistics and other aspects of your phd. Going to a completely unranked dept might mean much of that support is missing. Your peers will likely be less active or of a lower caliber, and they can potentially affect you as peers.