Google News is a bit of a blackhole, that is very expensive to feed with varying results. I am very familiar with how it works. As for getting accepted, give it a go, the worst they can say is no.
However, If you're not a "real" news site, don't set your hopes too high.
The reality is that just because you get accepted into GN, that doesn't mean sh*t! Now you have to be able to crank out content fast, and have the publish current news on topics that are trending, otherwise few people will find you via GN. Simply put if it ain't trending, there is no traffic. Think of it like old timey newspapers (ya know those pieces of papers with little letters printed all over them), the first source with the story gets the readers. Now it's obviously far more complicated that that with GN, but that ranking factor still holds tru as one of the more important, among many others.
So then let's just suppose that your riding goofy foot on a big trending wave of a topic, and your story is released right as all the bigger outlets are rolling theirs out, heck even beating several of them to the wave. Now if your lucky, you get placement on the home page closest to your topic, say sports. Your post will then rotate thru along with the notable authority brands like SI, CNN, Yahoo Sports etc... Then if you don't happen to be one of these brands your CTR will be less, of course helping to rotate you right off the home page. The same will eventually trickle down to the realtime coverage, and further you fall into the abyss of page 2 and beyond.
That's not to say that you couldn't hit paydirt on GN, and when you do, it's similar to any other social buzz.. Cause it does happen every now and again.
In the end, I would say just focus on creating useful content, if you're in GN, then it's just one more possible traffic outlet. Like all things G related, don't get be surprised when it doesn't reap huge rewards. Rewards are rewards not matter how big or small
I could go on for days, but thought I thro in a few cents.