There was nothing in a "cache that needs to be written to disk" in those days that I am aware of (certainly not in the days of System 1.0). And so, if you lost anything when you shutdown with a floppy in the drive, it would be unsaved changes in whatever app you had open at the time.

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I highly doubt it that the Apple programmers at the time didn't implement an in-memory I/O cache. I see it as more of a necessity for floppy-driven systems since you wouldn't want to wear out the floppy by writing to it every single time the user opened a window, renamed an icon, or moved an icon. All of these actions occur quite often (especially opening a window), so you wouln't want to write that to disk the exact moment it happened, every single time.