A lot depends on the publisher.
If you're working with an e-publisher or a small press, your cover preferences are more likely to be heard, though they may not be acted upon.
And you can make your suggestions at any point after you sell the ms.
If you're working with a large print publisher, however, you are dealing with a bureaucracy.
Your editor and the marketing person who makes decisions about the cover may never sit down and talk about cover design, face-to-face, at all. Your editor may have very little input into cover design.
What you can do to make your cover suggestion heard ...
1) ask your agent if it will be possible to negotiate a clause in your contract that calls for author input and, hopefully, approval for the cover blurb, (a good idea anyway,) and author input for the cover.
You may not get either, but see what your agent thinks about trying for them.
2) After the contract is signed, talk to the editor about your ideas for a cover ... recognizing that the editor is likely to defer to marketing on this.
The best time to submit an actual cover concept is probably when you send back your corrected ms.
That's the stage where your editor sends the ms, author bio and photo, synopsis, etc., to Marketing.
The Marketing folks who will decide on your cover cannot do it before this point.
This is the first time they've heard of you.
Ideally, you want your cover concept to arrive along with the rest of the packet your agent zips over to Marketing. It should exist in both hard copy and a computer file. If you have 'photos' of what your characters look like, that can be part of your concept package.
As to sending a bound 'book' as part of the submissions packet ...
(shrug)
you have an agent; take his advice.
Including a bound, self-printed book in the submission
-- look, this is only IMO and I'm respectfully disagreeing with posters above --
but I think it yells 'amateur'.
It's 'kittens on the letterhead' stuff.
This is not how the business works.
If agents and editors wanted bound books included in the submission, they would ask for them.
'Amateur' is not a huge mark against you in a market where there are many fine writers who are, for the moment, novices. But it's not really a mark in your favor.