IF your potential new employer is recommending you take a car loan to "force their hand" ask her to guarantee the loan - otherwise, if the new job falls through, you have a car loan you can't repay, and you will not be leaving the country until the debt is settled. And yes, your bank will know you are leaving because if it is the same bank your salary goes into, you will be required to get a bank clearance letter from them to give to your current employer to show you have no outstanding debts.
There is no obligation to give you an NOC
IF your potential new employer is recommending you take a car loan to "force their hand" ask her to guarantee the loan - otherwise, if the new job falls through, you have a car loan you can't repay, and you will not be leaving the country until the debt is settled. And yes, your bank will know you are leaving because if it is the same bank your salary goes into, you will be required to get a bank clearance letter from them to give to your current employer to show you have no outstanding debts.