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I have been assuming that when I depopulate a board and they break into several pieces, the board pieces will still be accepted as low grade board. Is that a fair assumption?

That is assuming the pieces still have something on them.

Depopulated boards will get downgraded and broken (but still populated) boards will also if it's not clear what they are and that all the board is there.

It sounds like you're basically talking about depopulated/blanks though; so most likely, yes, low grade.

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My grades are my own opinion and not an official grade from Boardsort

The idea on depopulating low/mid grade boards is to take the remaining IC's and leave the non-ferrous materials behind so it remains a low grade board. Large heat spreaders and Cu coils too, for the nitty-gritty scrapper.