Just wanted to share for anyone considering this since when I was searching for this I didn't find much.

It's totally possible to sleep train with your baby in a floor bed. A is five months old and had crappy sleep habits (even before we moved him to his montessori-style room). We connected with a sleep consultant who recommended putting him in a crib (among other things). We stuck with our gut instinct and did not use the crib.

A sleeps quite well on his floor bed, doesn't get off in the middle of the night, has learned better self-soothing techniques, and is starting to sleep longer stretches as night.

Success!