As long as the instances who's content you're trying to interact with are federating with your instance (beehaw), then you can interact with everyone, yes. It's important to keep in mind instances can choose to not federate entirely, or selectively block certain instances from interacting with theirs, although this isn't something you should have to worry about.

A good analogy I'm seeing thrown around is email: everyone has their own email provider - gmail, yahoo, outlook, or a corporate email server, etc - but all of those can send and receive emails from every other one. I have gmail, but I can email you at yahoo, and recieve emails from my friend on hotmail. If gmail starts being shitty and corporate or making decisions I don't like, I can switch to a different provider, and crucially, gmail doesn't get to decide how the rest of the email universe behaves.

Lemmy instances are like the email providers, and "sending emails" is like interacting with communites on any instance. If my Lemmy instance starts serving ads or something I can just leave it, and still have access to all the other communites on every other instance.