Short answer: It depends on the judge.
Longer answer: See, for example, FDIC v. Cheng (1992, Northern District Texas).
Multiple defendants, including Shearson Lehman Brothers and several of its employee bond-traders. Shearson hired attorneys for everyone. All defendants entered into a JDA. One defendant D also hired his own attorney, who negotiated a secret deal for him: he cooperated with prosecutors for a couple of years while in the JDA. When Shearson et al. found out, they screamed bloody murder. The judge expressed his distaste for the “degree of deception” involved but nevertheless allowed defendant D to keep his deal, offering the other defendants only the possibility of suppressing privileged information at trial.
Does that address your question at all?