I am currently on H4 and I have an employer ready to file for my H1. I was on an H1 before I went to H4 for about 2 years and so I do not fall under the quota. My employer told me that I can start working on an H1B receipt but I strongly feel that I can not and that I would have to wait for the approval based on H4 to H1 portability. Can I actually start working on receipt without an approval? If I do that, what happens if my H1 petition gets denied? Do I fall under the same visa I was before I applied for my H1?
No. You cannot work without your H-1B petition having been approved. You could have only done that had you now still been in H-1B status and were changing employers, which is not the case in your situation.
If your H-1B petition gets ultimately denied, then yes, you will fall back under H-4 status, as long as it will stil be valid on its own merits (i.e. your spouse will still be in valid H-1B status and your H-4 is still valid.)