Not exactly. It is used when somebody is successful at the first attempt. For instance, you're playing with a slot machine, but you don't earn any money and stop playing. Then, somebody goes to the machine, inserts a coin and earns a lot of money: llegó y besó al santo.
Another example: you go to a foreigner country. The first day you are there, someone offers you a very good job: llegaste y besaste al santo.
I guess its origin is due to the congregation, when they wanted to give a kiss to the image of a Saint. They used to wait for a long time in a queue until they arrived to the image. If someone was able to arrive to the image without waiting in the queue, because at that moment there weren't so much people waiting, él llegó y besó al santo.