Technically this should be possible. Blob Storage allows you to upload your file in chunks and once you're done you can commit these chunks in a specific order:
- PutBlock: Upload a chunk
- PutBlockList: Commit a list of chunks in a specific order
With these methods you can for example create a buffer in memory which stores the video and call PutBlock each time the buffer reaches a certain size. Then, once the recording is done you can call PutBlockList to commit all blocks. As a result, your blob will contain the complete recording without saving it to local disk first.