This ended up a bit longer than planned, so I hope you get some useful information out of this mess.
Simple answer is yes, it can be a viable choice. I have friends who made best seller lists in their genres with self published books. Self publishing is a great option for many authors these days. Harder answer is maybe, because while it's a great option, the market is flooded these days. Many self-published books, especially by first-time authors, languish and don't make back their editing and cover fees.
First thing to consider before self-publishing is why the literary agents aren't interested. This can be tricky if you're only getting form rejections. You'll need to get some eyes on the manuscript and try to pin down what is making them pass. The one thing you don't want to do is put the book out there if it's simply not right or marketable. This can be the hardest part, because it's next to impossible to be objective about your own work. Find readers who aren't afraid to hurt your feeling and get as much feedback as possible before you move forward.
I've done both self publishing and have published with small traditional press. For me, the pros include time frame, higher royalty payouts, making my own schedule, retaining all control over rights, and (after the Ellora's Cave debacle) not having to worry about the publisher's business standing. The time frame is adjustable to your needs. You can release in twenty-four hours or set up a pre-order for promotion time. I consider this a pro because I like getting stuff done and off my to-do list forever. For books over $2.99 (US) most distribution sites will pay out royalties in the 70% (cover price) range for digital. The higher-paying small digital presses tended to be about 40% net and most I considered were closer to 30%. With self-publishing I can schedule my book releases as I want them, release a series over time or all at once, depending on how i want to market. I can decide how to release or not release, pull the book or expand distribution, even hire an translator and do an international release if I want.
My cons list starts with how much more work is on my plate for self-publishing. I have to do all the grunt work--hire out for editing, arrange cover art, formatting, choose distribution and get the final copy uploaded appropriately. I have to manage all promotion and make review arrangements. Instead of one nice, neat paycheck from my publisher, I have small payouts trickling in from several places. My releases with a publisher had strong sales based on the publisher platform. I don't have that advantage when I self-publish. I've consistently made less money with self-publishing than with traditional publishing. There's also the question of knowing if the manuscript is marketable. I think my time with a publisher gave me better perspective on my own work, but I still won't publish without running it through a trusted reader.
My personal choice for the near future is to self-publish, because it fits my life better. I know I won't make as much income this way, but for now, I'm okay with that. In the future, I would like a mix of traditional and self-published books, but for now, I'm sticking to self-published.