Yes you can do "the train" exactly as described. I have seen it done a few times and have heard comments from many who have seen them. It will be ridable but will understandably require more control from the captain than your single or even a tandem.
You will probably have to take corners a little wider. I know I have to with my tandem and trailer configuration. I will be going for a tandem, trail-a-bike, trailer hookup within a year.
My #1 (7 yrs) is a little more aggressive and will ride solo or on the tandem. #2 (5 yrs) on the other hand hardly rides solo at all, but will fight to ride stoker. That does not bother me because we are all out there having a good time
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Enjoy your hookup and be prepared for a new nickname in your "hood". A neighbor told me that I am now referred to as that guy with the big bike and the trailer.