Yes, it is!
After the copy, just make sure the system folder is "blessed", i. e. it actually has a system folder icon. If that's not the case, you can simply "re-bless" it by taking the Finder (or the System Suitcase) out of the folder, and back in.
Edit: after re-reading your post, I have second thoughts. If the system that's already on your Mac is a complete install, it may be well be too large to fit on a floppy. You could manually strip it down of unnecessary stuff, but it's probably easier to just download a startup floppy image from Older Apple software downloads.