Nope. You'll be fine on whatever you're running on. Even Webrick.
Passenger takes care of keeping your application alive, makes sure slow clients don't break it, automatically handles concurrency and has low latency. That's just the basics, there's a lot of configuration options for the more serious deployments.
It also probably means that the server is on a $5 VM, so memory pressure is also a concern.
Passenger and Puma (from Passenger): https://github.com/phusion/passenger/wiki/Puma-vs-Phusion-Pa...