I'm not sure what you mean by this last sentence. But Git always computes the SHA1 of incoming objects (that's how it knows that the SHA1 is; the other side doesn't send it). And it likewise confirms that it has every object which is referenced by the newly fetched history.

The fsckObjects settings are entirely separate from the SHA. They are about syntactic and semantic rules in the objects themselves (e.g., well-formatted committer name/dates, tree filenames that don't contain "/", etc).