In general, how long does it take a traditional publisher to approve/disapprove your manuscript from the time you submit it to them? The literary work is fiction and is about 330 pages.
Also, is it a good idea to submit to more than one traditional publisher at a time? Or, should you wait for rejection, then try again somewhere else?
Should you have an agent?
The number of publishers that will even accept unsolicited fiction manuscripts is very small, so unless you are submitting to some very specific niche market, it is hardly worth talking about.
Most major publishers will only accept work that is submitted by agents, so basically you need an agent to submit at all. Agents have relationships with editors. They know what editors are looking for and so will save you a lot of unnecessary time lost in submitting to editors that were never going to buy your manuscript in the first place. They will also negotiate a better deal than you would ever be able to get by yourself.
There are other ways to get directly to an editor, but these basically mean that your manuscript has been solicited by the editor. If you pitch to an editor at a conference and they ask to see your manuscript, it then becomes a solicited manuscript. If you are referred to them by a writer friend they respect or owe a favor to, then it becomes a (reluctantly) solicited manuscript. If you self publish a book that sells a million copies and every publishing house suddenly wants your next book, it becomes a solicited manuscript. If you are a megastar celebrity whose name alone can sell a book, then they will pursue you and it will become an (eagerly) solicited manuscript.
But in any of these cases, you probably want an agent anyway to negotiate a better deal for you, and to take the business side of things off your hands so you can write more books.
In any of these scenarios, except the last two, however, you are still looking at months to get a reply.
Check the publishing houses guidelines. They will give you an idea of what they are accepting and from whom. An agent is nice, but it can be hard to get one until you have a contract.
Science Fiction Writers Of America, SFWA has an excellent site that provides info on various publishers and agents: http://www.sfwa.org/other-resources/for-authors/writer-beware/