Can I use store-bought custard for Portuguese Tarts?
Short Answer: Probably, but it won't taste as good.  

Longer Answer:
Given that most packaged custards (if you mean the powdered sort such as Bird's or Jello) do not contain eggs, you might find that the custard does not behave quite the same and certainly will not taste as rich.  They tend to use yellow food colouring to give the bright yellow colour that you would get from the egg yolks. It's a bit like asking if you can substitute Cool Whip for Whipped Cream.  Yes, but....