In its current release, it doesn't. It only allows to make a full convoy, and to change difficulty.
I'm working on adding characters right now, but I've encountered an issue, and I'll update until it gets fixed. The convoy gets zero'd (empty items), and the Barracks is cleared, too. Once I bypass these issues, I'll release the next build, which will be capable of adding any character back in (or even several of the same).
Can't wait to try that out! Will it be only the main units for now? Would you be able to have SpotPass/DLC characters added in too?