For those unfamiliar with the mechanisms of a pelham bit it's pretty simple. A Pelhams has room for the attachment of two different reins, the bottom one activating the curb and the top activating the snaffle. Activating the curb puts pressure on the bars of the mouth, the chin, and the poll (and the roof of the mouth if it has a port). The snaffle works like any normal snaffle on the bars of the mouth. They are very much like a kimberwick, however they have more flexibility because you can choose when you use the leverage and when you don't.
Converters, to my understanding undermine the flexibility of the bit, as they always activate both the snaffle and the curb. In my experience they are used by beginner riders that find it too difficult to use double reins, which leads to a horse being in a harsh bit with inexperienced hands (Though that's opinion since I personally don't think leverage bits are appropriate for beginners). I could be wrong, as I have never actually looked into the much since they are illegal to use in the USEF shows.
I'd actually be interested in hearing if they do provide any benefits and how they differ from a kimberwick as far as mechanisms go. After people responded I looked online and was unable to find much about bit converters. I'd actually love to learn anything more about them.