Travelling with a bike box from Milan to Aosta

Looks like you could if you took regional trains from Malpensa to Aosta. The Malpensa Express train to Milano Centrale is open type carriages with room. The regional trains from Milano Centrale to Chivasso and to Aosta are both marked

The bicycle transport service is subject to limitations. For details see the General Conditions of Carriage. Train with bicycle transport service accompanying the traveler.

Cost is 29.05 EUR (currently), although there may be a bike surcharge, and taking 4 hours.

On all regional trains – even those not marked with the special symbol – passengers are permitted to travel with a fully closed folding bicycle (even if not in the special bag) free of charge, provided that the size does not exceed 110 x 80 x 45 cm and does not cause danger or inconvenience to other passengers.
On regional trains marked with the special symbol, and limited to available spaces, each passenger can take an assembled bicycle on board with them, by purchasing the bike surcharge, which is valid until 11:59 p.m. on the date indicated on the ticket or, alternatively, another second class single ticket.
Train staff may not permit passengers to bring their bikes on board the train in the event that the transportation of your bike is deemed to be detrimental to the train service.

Thanks Sam, the tricky bit is that my bike box is larger than those dimensions. I don't know how rigorous they would be with this !