Yes, they need BP's (The child's seat assignment = 'INF').

However, having done a few RJ flights this year with our infant, there is nothing that prevents you from choosing a seat on the 'wrong' side, even when it's noted all over your reservation that you have a lap child. I did it the first time (not knowing that it was a one-side only thing until, as above, we were so advised) and had to move.

would be nice if (ha) .bomb was 'smart' enough to prevent it...but it is pretty far down the list (as it probably should be, given the other stuff they could fix) of .bomb bug-fixes/enhancements.