Yes, certainly! They would change at player discretion. The same process as usual will occur for a normal canon update (the 7-day rule, etc): your character will suffer a deep and overwhelmingly sudden urge to sleep whenever, wherever you decide. However, when you change alignment, your character will "fade" from sight into their new bedroom at the opposite court.

Thank you for bringing this question to our attention! We've added it to the FAQ to help future applicants.