My Situation
I am in a unique situation where I am working in a CPT status. I applied for H1B this April but was not picked in the lottery. After my opt expired on May I joined a CPT college and am working in the IT field through a desi employer. That technically put me in F1 status . I applied the for the TPS and have got the EAD till december for 2016. (I also have a MBA already). I am planning to leave the college as I already have my masters and going to college just to maintain my status.

My questions
1.I know TPS doesn't directly lead to GC. Can my employer continue to file for my Greencard while in TPS status (If i leave the F1 status.)????
2. What are the consequences that could occur if I get away from the F1 Status?

(I did some research and lots of sites related to immigration lawyer suggested that it was possible to change status from TPS to GC if the employer files for it)
some links
http://www.lyttlelaw.com/temporary-protected-status-tps.html
http://www.nolo.com/legal-encyclopedia/frequently-asked-questions-about-temporary-protected-status-tps.html