Can Train tickets be picked up/delivered to Hong Kong?

You mean the train ticket in China mainland?
If so, it cannot be picked up there. Ifyou book the HK Through Trains, you can pick up in person at Hung Hom.

But if you book the tickets with TravelChinaGuide, they can mail the tickets to your hotel in HK. By the way, the mail fee USD 5 is charged.

On the train page of TravelChinaGuide, you can search the train schedule and book the tickets.