When should I start testing?

So normally I would just take the answer of the wait 2 weeks until missed period but this month I have an oral surgery and I’ll be 11 dpo that day. They have to test me before so they know if they can put me under or if they have to do local anesthetics. Do you think if I’m pregnant at 11 dpo it will show or if it doesn’t show and they do put me under would baby be affected at all if there were one? They know I’m ttc and told me it’s protocol to test no matter what and just to keep trying then they would go from their test.