I don't think so. The first thing the unemployment office would do is contact your employer who will say that you are still on their payroll.
There are legitimate reasons for which you can quit a job and still claim unemployment (this seems like one of them), but you have to be able to PROVE it. Without any hard evidence, you end up in a situation where it is your word against your employer's and that I think is a battle few people win.
My advice would be this. Don't do anything immediately to lose your job if you don't have something else lined up. During those two weeks start looking for a new job, and contact someone in the unemployment office to see if you have a legitimate reason to quit and what evidence you should try and acquire to secure your claim. If those options don't work out, you still have a job.
I filed and lost an unemployment claim last year in Texas. My opinion coming out of that experience is that the system is NOT in your favor. I am not an expert about it, so please just take this as one person's opinion.