Yes, it will. Without the power source, the Wi-Fi box won't have anything to run off of. First, find a way to turn off the box from your computer if possible. If not, then I think most Wi-Fi mechanisms should have a Auto-Power button or SOMETHING... You might screw up your Wi-Fi mechanism by forcing it to power down.
Disconnecting a power source from a Wi-Fi box will not disable it. One of the ways to disconnecting this feature is by disconnecting the power cord from router. Otherwise, you should be in a position to move the box with no disconnection problems.