No, they will not do that. I was in a similar situation and they would not stamp the passport without the approval letter.
After listening to my sitiuation the the immigration officer looked up my A# to see if it showed if it was approved in their system. Since I had got the email just the day earlier, their system was not updated to show my case was being approved.
The lady made a comment like " if my system showed that u are approved, I might have considered your case" But you need a lot of luck to even hang around for 5 minutes for the office to answer any ad-hoc question like this.
No approval notice, no ticket no questions asked ...
