I did a speedrun, I have now found you can skip the fourth coin but it's really tight. The third may also be possible, The second one I got by mistake :P
If you roll into another section (the rooms with a transition and a letter marking them) of the Athenaeum library area, you get stuck and can't move until you do a sword attack.
Even after you find the lost boy and return him to his brother, he can still be carried with you. Not fully sure weather its a bug/oversight but it's what I found.