Data Capture.

The simple answer is yes, Wireshark can capture the data going through a wireless router. If you are interested in capturing over the air (i.e., using a separate laptop/PC to capture WiFi packets) then please read the following Wiki: https://wiki.wireshark.org/CaptureSetup/WLAN

Some wireless routers allow users to capture directly from the router using tcpdump or some other tool. If you do not want to capture over the air, then you might want to investigate this option.

I think Wireshark's role is better described as an analyzer of captured data. When it comes to actually capturing packets, usually the main challenge is in getting your system to 'see' the packets you're trying to capture (eg: for your wireless router, the challenge is to get all the packets the router sees in one place where you can perform a capture). Once you have a system that is receiving all the packets you want to capture, many tools (tcpdump, snoop, dumpcap) can do the actual capture itself. The power of Wireshark lies in its ability to help analyze the packets once they are captured.

In fact, Wireshark itself doesn't really capture packets at all. Rather, it calls on dumpcap behind the scenes when you perform captures in the GUI.

So, for the task at hand I wouldn't start by asking about wireshark. Rather, start with what is fundamentally a network question (how do I get a system capable of capturing packets in a position in the network where it can receive all the packets that I want to capture).

There are many solutions for that task depending on the network. As mentioned if you have a Wifi router that supports native packet captures, that's one way. Another is "SPAN" ports, or "port mirroring", where a switch will forward all the packets it sees from one or more ports and forward them on to another port (as a "mirror" port) so that a system running Wireshark can capture the packets and analyze them.