V + 기라도 하면 is used to show that an action has a very small chance of happening. It has two functions:
Negative: to express concern about what you would do if the event actually occurred:
주식이 떨어지기라도 하면 어떡해요?
If the stocks were to plummet, what should I do?
배가 더 아프기라도 하면 어떡해요?
If your stomach started to hurt more, what should I do?
신용카드를 거절을 당하기라도 하면 큰일이에요.
If this credit card were to be refused there'd be trouble.
TV를 가까이서 보다가 눈이 아프기라도 하면 병원에 가야 돼요.
If you did sit close to the TV and your eyes hurt, you'd have to go the hospital.
술을 그렇게 많이 마셔서 머리가 아프기라도 하면 출근을 못할 거에요.
If you did drink a lot like that and you got a headache, you wouldn't be able to go to work.
Positive: although the chances are slim, you are still hopeful that it will occur (used with얼마나 좋을까):
부장님으로 승진을 하기라도 하면 얼마나 좋을까...
How great would it be if I were promoted to head of the department...
첫번째 면허시험을 볼 때 합격하기라도 하면 얼마나 좋을까...
How great would it be if I were to pass my driving test the first time round...
시험에 최고 점수를 받기라도 하면 얼마나 좋을까...
How great would it be to get full marks in the exam...