For those who have experience (or some additional knowledge) with the Cambridge admissions process - is it generally the case that, at least by now, the school has sent off all of its offers, and that those who have not yet heard anything are likely to be rejected, unless a substantial portion of students do not accept offers?

I guess that is pretty likely....

I would not say so.
Last year the main bulk of decisions came out on 7-8 April, this year it has been said to be end March, so I do not think it is a matter of worry so far, especially given the fact that only a couple of people have confirmed receiving of acceptance on this site.
Wait, wait and wait....

No, your assumption is wrong. BOGS sends both offers and rejections at the same time. Many students are still waiting for the outcome (including me).

Thanks for the information, folks. Much appreciated!