Yes, an instance is launched on a compute node. That instance's root disk is (normally) an ephemeral disk on the compute node's local disk. When you attach a volume, cinder provides the volume from whatever backend is configured to the compute node and nova-compute takes care of communicating with the hypervisor to get it attached to the compute.

Your second question asks about adding storage to the compute through SAN/NAS and directly attach it to the instance. Yes, technically, you can do this. Semantically, OpenStack is just a collection of APIs that make it easy to interface with various backends and connect them together. If you have storage available to the compute node, you could tell the hypervisor (often via libvirt) to attach that storage to the instance. Nothing prevents you from doing that. Except, perhaps, root access. Your end-users will not likely have root access on all of your compute nodes.

Instead of bypassing how OpenStack does things, it would be easier to embrace the OpenStack way. Configure cinder to use your NAS/SAN as a storage backend and allow cinder to do the provisioning and allow nova to manage the attachments. Much easier in the long run.