Yes, it should take root, I've done it by sticking a snapped-off piece next to the mama plant.
If you wouldn't mind, please tell us about the conditions of your plant. I've kept one each of 2 colors alive for a year now, but they're frozen in time. One of the slowest plants here of so many others, no sign of making another round of cute little flowers like they had when I got them last year, around this time I think. Can't imagine it growing enough to even lean, let alone break itself off over the edge of a pot. Tried more sun (last few hours of the day,) less sun (just the first hour or 2 in the morning,) a little fertilizer. Supposed to like humidity and sheesh, definitely have that covered in southern AL! Does it actually need to be above 80% for it to be happy? Coming inside for winter was hard on it, even though we don't use an air-drying heat source, but it never has perked up outside again. If you could add a pic, that would be great too! I'm embarrassed to even show my silly little plants. I do have a little terrarium thing but the "pot" part is so small. Maybe Fittonia would prefer that anyway?
Good luck, Bev! You probably have some good advice too, care to share? If you have a BBS nearby that sells Exotic Angel plants, this is often part of their assortment.