May be I am not getting it. Once you apply for I-485, you are in the process of adjusting to permanent residence. Why would you still have F-1 or convert to H-1, I am not sure. I can see H-1, if you do not feel safe with your job, but even then, I-485 itself has a lot more protection than H-1 after you have passed 180 days. So I am not sure what extra benifit you are getting from that.
But to answer your question, you should let BCIS know everything about your status. In fact they already know, they are as disorganized in this matters as any of the third world nation. They may even be worse, but the fact is, if they want they can find it easily. So why take chances. I don't see any harm in informing them unless you have something to hide.
I am not an attorney. This is my opinion based on past five years experience in forums like this and by still going through the process myself. So don't take this as legal advise. Ask your attorney if you need.