Given that Dimmesdale dies before being able to escape to Europe with Pearl and Hester, in The Scarlet Letter, one can only assume possible answers to the question that he could find happiness. Dimmesdale is very different from Hester. His weaknesses are only balanced by Hester's strengths. Therefore, one could easily look at the possibility of happiness in two very different ways.
First, one could use the ever popular cliche: Opposites attract. Knowing how different both Dimmesdale and Hester are, one could believe that their differences is what has brought them together.
Second, one could argue that the differences between Dimmesdale and Hester are too great. Basically, they are simply too different to be able to find happiness with each other.