Braddock is an ideal anchor character- super tough, reasonably lethal, and with access to both precise and area attacks. She may not be first pick for soloing a lair, but she's perfect for holding the field while her squad mates recover, and her MAYHEM ability is a nicely low-effort way to clear out overcrowding. She's also a good mother hen to low-level agents, granting an XP boost (the only kind the game offers, short of jacking up the difficulty), and an automatic Fortify effect when she switches out them (a crystal core well spent).
Braddock's recruitment mission is availalbe after recruiting Rama in the main campaign.