Does this imply that data is replicated between the two forests?
Yes, but not to the degree you think of. Naturally certain elements will be replicated - those that are needed to maintain a trust relationship.
But no user level data. Stuff like passwords etc. do NOT leave a forest.
Can I perform searches on one global catalog and get results from both catalogs?
No. And if you think about it, it makes sense.
For example, the schemata of both forests can be different. If one object has been extended - what would the schema on the other forest do? Trust is not about syncing data, it is about allowing security contexts to pass.