No, if you have an instance and then you start an ECS cluster, it does not means that you'll have two instances.
EC2, as you already understand, is simply a remote virtual machine that you can launch.
ECS, on the other hand, is a logical group of EC2 instances on which you can run an application without having to scale your own cluster management infrastructure because ECS manages that for you.
If you have an instance, then you launch ECS, you'll have that one EC2 instance only. If you go ahead and register that EC2 instance to ECS then your instance will become a part of the ECS cluster but you will still have a single EC2 instance in that cluster.