I don't think there is any way that a consumer 'blocking' device could cause the BT engaged tone to be heard instead of ring tone. It could 'spoof' an engaged tone of its own, but the BT ring tone would be heard by the caller first.
My reasoning is that the consumer equipment only becomes aware that an incoming call exists when it detects the ringing signal, by which time the caller will already be hearing 'ring tone'. Landline networks actually go to some lengths to ensure things happen that way. The 'backwards path' is swiched into circuit before the called phone even rings, else there may be a tiny switching delay before the calling party hears the called party's voice.
Mobile networks must sacrifice that ideal due to airtime being a precious resource, which is why when calling a mobile, instead of "hello?" you often just here "..low?", or worse just "...?".