From what it looks like now, no it will not. From what we've been gathering, the device isn't even "hot" all the time on the network. It basically fires up at certain intervals and uploads the data/picture to the Bloomsky servers.
But Bloomsky supposedly has an API programming way of you getting to that data on the server. I'm hoping soon someone with some programming experience will give us a simple HTML code we can plug into our websites and post that data there.
But someone had figured out a way to get to the Weather Underground image. Through that image, you may be able to download a copy of the most recent image.