First, ConcourseConnect only works with PostgreSQL, which is a great reference platform as it has an agreeable license for redistribution, but I see your dilemma.
To get MySQL working, the PostgreSQL scripts would need to be modified for MySQL syntax. That's fairly straightforward and could be accomplished in a few days. Second, though, the application would need some adjustments to work with the MySQL syntax. I've done this before with other projects so I know it can take a week or two of development. After that, lots of QA.
Finally, MySQL would need to be supported in future development and that is why we've cut back on supporting other databases, like MySQL and MS SQL. In the end, it doesn't matter if MySQL is added to the development, but someone either needs to maintain it or pay for it to be maintained since we are quite pleased with PostgreSQL, although MySQL would be a good next candidate.
Does anyone want to sponsor the development and maintenance of MySQL compatibility?
Would you consider having Connect hosted in a PostgreSQL environment?