Ooh man, I did a ton of research on this one, and no crystalized sugar is not the same as unsulfured Black strap molasses, how ever I never found any info on it doing any harm to the plants, just don't contain the same amount of micro and trace elements, but will still provide the carps for your organic soil (if your in that ?)
here is what I had


I even used it a few times with no ill effect (deluded in some boiling water then added to the water Can)
but got me some real molasses from my wellness shop, less then 5$ for a small glass ..
pic of what I use in flowering in my soil/soil mix the glass contain the molasses (Bat guano is for tea`s and to mix in the soil, green sensation is just another Bud booster)