maybe, maybe not. Particularly if your account is followed by anyone with a platform that doesn't support DELETE from remote servers, like like earlier versions of Diaspora and GNU Social. and yoru delete command might not work such as if the remote server is down when the delete request is sent. Once you choose delete most platforms send a request to every server that it knows of to delete the same, if it doesn't get a response within a certain amount of time it will request it again, and after so many failures it stops trying. The server could later come back up and it never know that the item was deleted.
I'm not sure aware off hand of any servers that make it easy for admins to turn off the ability to delete, but its Free Software so anyone could download the source code edit it as they see fit, like removing the delete function, compile it and run it on their own server.
Its a really great reminder that we all should assume anything that has ever been posted on the internet will exist forever. So don't post stuff that is going to come back and haunt you.