I'm getting ready to start submitting a book I've written. I copyrighted an earlier draft of it a few years ago (as in submitted it for official registered copyright). The final draft has not changed much from that draft. I know from submitting poetry to publishers that publishers don't usually want work that's been displayed or published elsewhere. Do publishers care if something has already been registered for copyright if it hasn't yet been published or displayed?
If you live in a country that is a signatory to the Berne Convention (most countries are), then your work is copyrighted as soon as you create it, regardless of whether you go through any registration process. To a publisher, your work is already copyrighted, and if they want the copyright and not just publication rights, they'll have to ask for that in the contract.
If, however, you have assigned or relinquished copyright to anybody else -- for example, if you wrote something in the course of employment that belongs to your employer -- then the publisher will very much care, because it restricts their right to publish.
In general, you can negotiate with publishers over work that you fully own the rights to.
Ditto Monica Cellio.
Let me just add, registering the copyright before you submit it to a publisher would just be a waste of time and a headache. The publisher is almost certainly going to insist on doing some editing, making some changes. At which point the original copyright is no longer valid, as it's not the same content. So it would have to be registered again anyway, I suppose as a "derivative work". (I'm not quite sure as I've never tried to do things this way.)
Are you afraid the publisher will steal your work? This is really such a remote possibility that it's just not worth worrying about. Any publisher who did such a thing would quickly find its reputation ruined and no one would submit manuscripts to them and they'd go out of business. It's like asking how to prevent the bank from stealing your money. What if I make a deposit and then they take the money but don't credit my account and deny I ever made this deposit? What if auto repair shop steals my car? Etc. It makes sense to take steps to protect yourself from thieves and con men, but you can't live in fear that everyone you try to do business with is a thief.