At the open day the Adcom said they highly recommend people do the assessment day. They even said you should apply with planned assessment days in mind as this greatly accelerates the admissions process for you. From my submission to my admission I clocked 3 weeks. Compared to the 4 months I am experiencing for other schools that is just ridiculously quick.
I think if you live close enough to fly to Barcelona and don't do the AD it will definitely be detrimental to your chances. Also, keep in mind that there are Assessment days in NY as well and in some other city. Not sure when though.
But the AD wasn't difficult. It was actually sort of fun. Personal presentation - very straight forward, that took up half of the day. Case studies - very straight forward. I think it really is a chance to gain an advantage as it seems quite a lot of the people at my AD got accepted (before going I thought it was a disadvantage).
All in all I quite enjoyed the AD experience. Hope that helps!