Each and every pass "runs over" the older passes. Each pass writes data to all the drive's freespace once. So if you do a run with seven passes, freespace is overwritten seven times. Same goes for overwriting a file.
So I believe the answer to your question is "yes".
What's more, for most intents and purposes, one overwrite pass should be plenty--unless you might have certain agencies with three-letter acronyms for names after you, in which case I'd seriously consider physical destruction of the media in lieu of an endless series of overwrites. But that's me...
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