Yes, it is possible to record both the RGB and the Alpha channel at the same time.
(Note that you should use Realtime recording if you want to record a live physical camera input.
In this particular example however we are using a pre-recorded video input.) 

You can do it in two ways.

1. The simpler way is that you record the keyed footage with a codec that records the alpha channel separately within the video.

Such codecs are QT RLE RGBA, Cineform and image sequences recorded in TGA, PNG and TIFF.

So, in the Flow panel it should look like this:

Click on the Keyer__All node and make sure it is set to ADVANCED B Keyer Type in the Pin Values.

Next, click on the Video Recorder and make sure Alpha is switched to On, Framerate is set to Realtime and Video Format is set to QT RLE RGBA or Cineform or any of the above mentioned image sequence formats.

2. The second way is to use an Alpha Splitter and record the two channels with two separate Video Recorders.
It should look something like this in the Flow panel:

Please, note that to do this you need an Alpha Splitter node connected to the Keyer__All compound in order to split the Alpha component from the original RGB video signal.
This way you can connect both the RGB and the Alpha components of your video signal to a separate Video Recorder individually.

In this example we have used a Pin Collector special node (named Alpha Split rec on the screenshot above) to be able to press record on both Video Recorders at the same time.
We then added the Pin Collector to the Control Board.

Note: recording both components of your original video channel in Realtime with two Video Recorders is heavily dependent on your PC configuration. 

We recommend that you use H.264 or MPEG-2 to record both components simultaneously on lower spec machines. For bitrate about 3Mbps is a good starting point in terms of quality, but we encourage all users to try higher bitrates depending on their PC configuration. To set these values, click on the Video Recorder node and set them in the Pin Values panel. Don’t forget to set the file names and the output folders!

(You need to set the values for both Video Recorders individually.)