Short version: Cor and other mesh networking protocol cannot provide you anonymity. Use Tor if you want that and be aware of its limitations.

Long version: Anonymity is typically defined by the number of people you are hiding with. If your adversary learns something about you (e.g. your language + style) or the network (e.g. by surveillance), your anonymity will get lower. To avoid it getting too low, you want a big network which is as much outside your adversary's reach as possible. Mesh networks cannot provide either. They are often small and even if they are not, you will have to use a local internet uplink if you want good performance. Mesh networks are also radio based which makes them easy to monitor.

Also notice that:

Movement tracking

When you are connected to a mobile phone network, the network operator knows your location. Cor tries to make it hard for others to track your location. The theory is rather simple: You do not need to authenticate yourself. Then you need to prevent information leaks, which is hard: