I'm curious as to whether or not there's a way to use an authenticated Shopify user's web session to delegate authentication to a custom Shopify application? The behavior I'm looking for would be analogous to OpenID where Shopify acts as the OpenID provider and my custom application acts as the relying party.
You can't use customer accounts as an identity provider unfortunately.
What you can do is have them log into your app using the same email as they're using on your site and then pull all their info using the email as the key (assuming you do proper registration activation against said email to confirm ownership)