Hi all, I'm a non navy nuke(MM) but I worked in a conventional steam plant as the MMOW. I have 8 1/2 yrs experienced in this field. I'm currently attending LSU for Mech Engineering degree with a minor in Nuclear Power. I recently applied for the SRO position @ Entergy in Louisiana. It took some time but I received an email inviting me to take the POSS test for this position. I wanted to know what's the likelihood for me getting this job. I'm currently studying for the test and I hope I do well. I really want this job!! 
No one can really answer that. It is all on you. First, you have to pass the POSS test. Then, I am assuming they will have some sort of supervisory screening before or after the interview. How you perform in all of these is on you. So you really should be asking yourself, if you think you are likely to get the job. It is your career, go after it.
If you haven't STAR interviewed before, google STAR interviewing technique. I particularly like MIT's write up on the subject.
You will be competing potentially against Navy nukes getting out and previously licensed SROs, among others.
I am not well versed on the non-nuke requirements for instant SRO, but I am assuming that since they invited you to test, you must meet them.
Good luck and keep us posted!