I have made the trip by train.
I'm pretty sure all foreigners inside russia have to be "checked in" using the immigration paper you get when entering. (the piece of paper that slides inside your passport)
I think your main problem will be that it's very difficult to get a russian immigration paper by entering Belarus. You will have to be very very specific when you enter Belarus that you will be traveling to Russia so you need this additional paper. If you fail to obtain this paper then you wont be able to check in to any hotels inside russia.
At the border crossing, all I remember was the train stopping and some border guards coming thru. They were only interested in passengers with Ukrainian passports.