Well, yes. There are many ways to do this. Unfortunately, I'm not very well-versed in this. I wish I could help you more, but all I can really tell you is that it is quite possible. DiskOnChip may be a good place to start.
Yes, I've seen WinCE fit into a 32Mbit Flash chip, but it is not easy to do. It had to be compressed to fit and then decompressed and shadowed. The BIOS had to be redirected to look for the OS location in memory as opposed to floppy or Master boot record. After that I'm not sure what else was needed.
One thing I've been meaning to experiment with is the Boot ROM socket present on most network cards. These are used to load some initial network drivers and boot off a network with diskless workstations, and with some work one could get a flash or EPROM chip to boot from this socket. I've never tried this or looked up info on it, but it may work for your application.