A Few thoughts...
Hi,
The difference between going to school on H-1B and EAD.
1. On H-1B, you cannot attend school as a FULL TIME student. For that you have to convert to F-1 status. You can only go to school part time but you should be primarily working( that way you are maintaining legal visa status).
2. On EAD, you can go to school FULL TIME, without working, though you may not want to state this to INS because the intention of issuing an Employment based green card is for future employment.
So if you go to school after obtaining your EAD, it may not cause problems until INS issues an RFE for Pay stubs,W-2 and employment letter. At that point of time, if you are able to prove to INS that somebody is willing to hire you, then you'll be able to get your GC without any problem.
But if your case gets transferred to the local INS office then they may want to see you being employed with some company.
Hope this helps.