Does the patrons get notification when a post is published in wordpress?

Like how the patreon sends notification to the corresponding patrons based on tiers when a new post is published, can it be done same when we post in wordpress locking in with patreon tiers?

Currently there is no mechanism to do this. If you have any mail plugin that sends an email to site users when you post a new post at WP, that would accomplish the same purpose.

Can we submit this as a feature request? It makes so much sense and I do not want to spam users via email when this can easily be done via the APIs of the sites.

My workflow is heavily inside the WordPress site, not the Patreon page. Would be a benefit for all users to publish a post, restrict it to patreons with the WordPress plugin and these links are added to the Patreon posts page on the Patreon site.

Implementing mail notification capability into the plugin is a bit tricky in that many people may be using existing notification plugins to do it. You could use an existing notification plugin that allows you to add a condition to notifications - ie look for a certain user meta key etc.