If draw down is within weeks they probably won't check ICB again as all underwriting criteria would have been completed. If draw down is months away mortgage co may look for updated information. Things have changed a lot though and I'd be wary of jeopardising the mortgage unless you have comfortably passed all underwriting criteria.
You could try get loan approval from the CU but don't drawn down the loan until after mortgage draw down - any problems from mortgage co forget the CU loan. I don't think anyone on here can say with certainty that the mortgage company won't do further checks before they give you the cash.