Just wondering if I sent a manuscript to an publisher based in lets say the states, would I need to live in the states for my manuscript to be considered?
Yes you can. In fact, people do so all the time. I am Canadian. I have published one book with a European publisher, one with an American publisher, and have another coming out from an American publisher later this year. I have also contributed to two other books from American publishers and had a number of articles and stories published by American and British periodicals.
Some things to be aware of:
Publishers don't necessarily publish to a worldwide market. A book may be published by different publishers in different countries. Be aware that your original publisher will certainly try to take a piece of action on these foreign rights sales. One of the reasons you want an agent is to navigate these waters for you and make sure you get your fair share of the revenues from each market.
If there is something about you or your book that would make it likely to sell more copies in your country than elsewhere, you may want your first publisher to be in your own country since if it is published abroad you may only be getting foreign rights money for sales in your own country. (This has been an issue for Canadian authors published by American publishers in the past.) Again, you need an agent to help you navigate these waters and get the best contract you can.
In some countries, publishers get subsidies from the government. Such subsidies are almost always restricted to the publishing of the works of citizens of that country. Therefore it may be impossible to place a book with a foreign publisher who relies on government subsidies. There is usually no law that says they can't publish you, but the economic model is much less favorable for them.
I have come close to publishing with a small press outside of my home country (Australia); so it's definitely possible to have it happen.
Also keep in mind that a lot of the small press publishers are being bought out by the big companies though, and being relabeled as 'Imprints'.
So, yes, you can definitely send your manuscript overseas for consideration, especially if they accept e-mail submissions.
Also, keep in mind that a lot of the big publishing houses do accept unsolicited manuscripts in different programs and a lot of the time they have localized offices in a lot of countries.
It just depends who you want to publish with and in which country.