I'm in Texas. I've never experienced this myself, and haven't ever had to apply for unemployment benefits (knock on wood), but I know plenty of people (5-6 in as many years, all with different companies) who have been fired or laid off and none of them has ever received unemployment, even after fighting their former employer on it.
My point is that you should NEVER count on getting it, and especially not with getting in quickly. I got laid off in Michigan and was eventually accepted, but by that point I had burned through all my savings (I was pretty young, so there wasn't much to burn through) and already accepted a job here in Texas. It was a nice bonus, but didn't really help me with my unemployment situation in any way.
My point is that you should NEVER count on getting it, and especially not with getting in quickly. I got laid off in Michigan and was eventually accepted, but by that point I had burned through all my savings (I was pretty young, so there wasn't much to burn through) and already accepted a job here in Texas. It was a nice bonus, but didn't really help me with my unemployment situation in any way.