Is it possible to host an ECS cluster with p2 or other GPU instance types?
You can use custom instances of any type with ECS -- the key is running the ECS container agent on the instance of your choice. So, in general, I followed this documentation on that process with success -- http://docs.aws.amazon.com/AmazonECS/latest/developerguide/ecs-agent-install.html -- but do note that you probably want to also specify the ECS cluster into which the instance goes (otherwise it will go to "default" cluster).

To specify the cluster you specify env var ECS_CLUSTER, typically in /etc/ecs/ecs.config prior to running the container agent. See here.