You can, but you'll need a separate piece of software to run on your computer and FTP the images to Sensr.net. You can use any software that will FTP the images, but we've tested EvoCam and CamSpinner on the Mac. There are a number of options for Windows as well. Take a look at the Stand-alone Programs section of Cowboy Frank's Webcam Software page.
While PC cameras will work, Sensr.net is designed to support network cameras that connect directly to your home network. These cameras don't require a computer to be on in your home at all times. Since they don't have to be connected to a computer, you have a lot more flexibility in where you can locate a network camera as opposed to a USB camera.