No, types are database bound, and can only be referenced within that database. For example, on my environment:
USE Sandbox;
GO
--This fails
DECLARE @test-2 Assets.app.OrderItems;
GO

USE Assets;
GO
--This works
DECLARE @test-2 app.OrderItems;
GO
If 2 or more of your databases both need to be able to use a Custom Data Type, you'll need to create it on both databases. If all of them do, then you'll need to create it on all of them (and I suggest you create it on the model database to, for future databases).