We do have a Slack integration that notifies project members when some modifications were made to their project; however, you can’t “manually” send updates and updates will only be sent under specific circumstances. You can learn more about it in this handy article: Slack + Asana • Asana Product Guide
Currently, our Gmail addon only allows you to create content from your Gmail to your Asana; it does not work the other way around; you can also take a look into this third-party integration, but I’m not sure this will answer your needs too!