Hello @findingbugs, as you said in your question it is absolutely correct that we can use VPC Peering provided by Amazon to build a private connection between your VPCs.
Coming to your question,
Yes, it is possible. You can build a connection between two VPC in different region.
Taking an example of EC2 instance trying to connect to a DB Instance.
Your EC2 must use public IP.
Your Db Instance must allow public access, i.e. it must be in a public subnet.
You must give public access while you create the DB Instance.
Note:- Both your VPC must have public subnets with Internet Gateway attached to the route table, else they won't be accessible.