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Yes, if the traffic is sent unencrypted and you can actually capture it.
If the "someone else" is connected to the router via a cable you probably won't be able to see the traffic as it's likely that the router is also a switch. See the wiki page on Ethernet Capture for more info.
If the "someone else" is connected to the router via WiFi, then you might be able to capture the traffic and you might be able to decrypt it. See the wiki page on WLAN Capture for more info.
