I routinely get Amazon in the UK to deliver items to my son's address in England without any difficulty, and get items delivered to my daughter's address here in Australia. My experience is that they will ship to any address that you nominate when you are placing the order.
I would be careful about customs and excise duties, but given what you are suggesting would see the items effectively remain in the EU, that shouldn't be a problem. On this, Amazon had to set up Amazon Australia several years ago in a way that dealt with Australian sales tax changes that had come into force, resulting in direct importing becoming less attractive.
As
@Tincatinker suggests, confirming a suitable delivery address would be important. For example, don't expect a hotel to collect an item from a post office if the parcel is too large to be delivered as part of the normal post. You might find that even if the hotel does agree to hold the item for you, only a delivery note is sent to the hotel, and you will have to collect the item from the post office where the parcel is being held.
At this point, be aware of any time limits on holding items for delivery. Post offices and other parcel delivery services all have various time limits on how long they hold items for collection. Post offices typically are two weeks, but I have been lucky and they have held things for a little longer. My wife has found when she has been arranging parcel delivery when travelling overseas that there are shorter hold times in some places, and she has had to arrange for someone to collect her parcels because she couldn't be there to collect them herself.
I don't think Amazon will be the challenge, but these other things might.
