I am curious with current technology and tools, are we capable to sniff up and down stream of any open/closed wifi router without connected into it?
At first - strictly speaking - your wifi router is most likely two things. First: A wifi switch and second a router (and probably a lot more). The thing you want to attack is mist likely the wifi part as you state you dont want to initiate a connection.
Since wifi is no strictly directed method of message sending, packets will be broadcasted and that's it. So: If the wifi is unencrypted you can simply use a wifi-card and put it in "monitor mode". That means it will simply accept all packets flying though the air. Since everything in an open WiFi is plaintext you can read the contents (until transport encryption kicks in). If the Wifi is encrypted you can do the same as well but you will only get encrypted content. Under certain circumstances decryption after capturing is possible (see Wireshark-Wiki). You will need at least need to know the AP's SSID and PSK for that.
Yes, Wi-Fi technology are radio-waves following the 802.11 standard by the IEEE on different channels, the most common being 2.4 and 5 GHz, but also comprehend some other frequencies.
The 802.11 standard provides several distinct radio frequencies ranges for use in Wi-Fi communications: 900 MHz 2.4 GHz, 3.6 GHz, 4.9 GHz, 5 GHz, 5.9 GHz and 60 GHz bands
From: Wi-Fi - Wikipedia
Since the antennae aren't suppose to "hear" all radio waves, they operate on a "Managed" mode to accept only packets of information directed to you (Has either your MAC or IP - depending on the OSI level)
To be able to "Sniff" Wi-Fi packets you need to change (if the hardware/chipset allows it) the antenna mode to "Monitor" (Which will allow to accept/hear all packets) and use a software to read the information coming in, like the most famous Wireshark or aircrack-ng, ettercap, etc. or any other packet analyzer
All of this is possible without starting a connection to any network.