tl;dr, yes, it does.
Containers are nothing like VMs, and containers in Linux are basically a combination of a feature called Cgroups, which allows to restrict the resources (like memory, etc.) available to a process or group of processes, and namespaces. Namespaces are a construct in which certain namespaced resources are separated from each other, and processes can only see those belonging to their namespace. A simple example is a mount namespace. When you launch a container, you see a / directory which is not the root directory of your system.
Now, the problem is, that not all the resources are namespaced, so there is still quite a lot that processes within containers can do interacting with the main system resources, especially if they are root.
A root process within a container generally can do lots of things that the actual root process can do outside of it. For example, mounting parts of the filesystem (if you run with --privileged), loading kernel modules, etc. Podman can run rootless, in the sense that it uses also User namespaces, meaning a user 0 (root) inside a container is actually mapped to something else outside, but also docker nowadays can do the same.
So yeah, in general, running the applications with the less amount of privileges is a good idea and you should do it whenever you can. Even if you do need some privileges, you should add only the Capabilities needed, not just go straight to root.