not with irrlicht. Irrlicht uses zlib for reading zipped files. I do not know if zlib has write capability (check the links page to find a link to zlib). If it does (and I think it doesn't, but it might) it would probably be possible to expose the zlib interface in Irrlicht and allow writing. But that's all just conjecture. Currently it cannot be done
You do a lot of programming? Really? I try to get some in, but the debugging keeps me pretty busy.
zlib has both read and write interface. But zlib does not offer zip archive functions. It can only compress one file each time. All archive handling is implemented within Irrlicht. Thus writing one file (similar to UNIX *.gz files) is easily done, for all other things you need some additional functionality to be implemented.