A:Answer If by "continuously" you mean you want it recording all the time so you can review the video to check the weather from any time during the recording, then yes - BUT:
1 - You'll have to buy a subscription to their cloud service to store that volume of data.
2 - You'll need to train a primate, or invent a robot, to replace the batteries frequently.
Actually, you really need an AC powered camera for this to solve problem #2.
As for problem #1, the best solution would probably be to have your wired camera connected to a DVR that you could access via the internet to review the video. Plus the relevant software to interface the two, and allow you to control the recording(s).
Which, in reality, probably means you need one of the proprietary DVR based systems...sorry.