Does Telegram allow for members who have it installed be pinged every time there is a new piece of content from admin? Is there a way to manually tell the system to do this?

Hi there. Telegram, Fb Messenger, and Email will send you a notification when there is a notification on your in-community notification center (the bell sign). 

Now, let's see when there is a notification generated for a user. It is explained here81. 

This is86 the suggested way if you want your users to receive a notification when there is a new content in the community. 

So, there is no native way to say that every member in the community should receive a notification when an admin posts something. However, as a workaround, you can post that content in a group, add the group as default, then turn on the notification for the group. Whatever gets posted in that group, everyone would be bale to receive a notification.