Hi there richardo3,
actually you are wrong. The bank cannot tell you if your BD is chased, because they do not keep the money in some bank account. When you deposit the money, they keep it in some temporally account until the end of the day. At the end of the day they deposit all gathered money from that account to relevant Canadian account which is own by CIC. From this point on, your bank has no clue what is happening whit the money. Therefore it will no be slower process compared with the CC payment, because actually when they start to look through your applications, the money from BD are already in their account. I am not sure if your Bank sends official asking to the Canadian Bank about: BD number <bla-bla> "What is happening? Is it processed?" and etc. Will the other bank provide real update about that ??? Not sure. May be yes, may be not. But I am almost 98% sure, that if go and ask your bank to send official letter to Canadian bank asking about your specific BD, they will tell you something like "Sorry sir, there is no chance to provide you such information. It is out of our scope"-or something like that. So to conclude everything, in my opinion there is almost no chance (except if you have some real close friend in your bank, who owes you big favor) to receive any update regarding BD process.
Good luck to all!