No and no.
Second point first. Many agents, if not the majority, are willing to consider unpublished authors. Few of them are willing to shut the door to the next big thing. You also have to be realistic and understand that apart from agents just starting to build their list, they aren't going to take on very many new names in a year, but it happens. Depending on the agent and the year, I'd say between one to ten new clients in a year. That's a guesstimate, of course, based on what I've seen agents report, and will vary wildly depending on several major factors.
Now the first point. Large publishers with very few exceptions will refuse to look at unagented submissions or even queries. You stand a better chance with small, independent (not to be confused with vanity presses) publishers, BUT...
It's better to start by looking for an agent. First, agented authors make more money, even taking into account an agent's commission. Second, an agent will likely be able to head much faster for editors who actually want your kind of work. It's their job to know such things. Third, and sufficient unto itself, if you shop your work to every agent without success, you are still free to look for a publisher on your own. The reverse is not true. If you shop your work to publishers and they turn you down, agents are not going to touch you. You've burned all the markets. If you made newbie mistakes in the process (like mistaking harassment of publishers for persistence), you may have burned them long-term. Much better to have an agent standing in the way of the more egregious mistakes.
I would suggest reading some agent and editor blogs to get an idea of how things work, and what their day-to-day life is like. It can be quite an eye-opener to realize, for instance, that phoning an agent who hasn't already signed you up is a major faux pas. This isn't at all obvious to someone who doesn't know what an agent's day is like and it's very good stuff to know. Topnotch agent blogs are: Nathan Bransford, Rachelle Gardner, Chip MacGregor, Jennifer Faust, Jennifer Jackson, Janet Reid, and the much-lamented Miss Snark. Never mind that most of these wouldn't represent Christian fantasy; most of the info is generic and very useful.
Glad to hear your betas are reacting well; that's a good sign. Don't tell an agent that though. They don't care. Unless they know your betas personally and trust their opinion, it means about as much to them as saying your mother loves you.
Whatever you do, DON'T consider Publish America. Before you consider much of anybody, check the Bewares forum here, for that matter. There are all kinds of scam artists willing to sell you your own dream, some of them agents.
