No not all instances, unless you write a script using their API.
The public timeline of all instances is by default public, without authentication. So technically you could scrape them.
Also I must advocate relaying. ActivityPub relays are very simple servers that receive all posts from any subscribed instance. Not just mastodon either, multiple AP services supported.
And then relays those posts to all subscribed instances.
Relaying does wonders for the public timeline of a small localized instance.
