That's what the U.S. Court of Appeals for the Second Circuit just held today in U.S. v. Stein, in a case involving the prosecution of 13 former KPMG partners and employees. "We affirm the district court's ruling that the government deprived Defendants-Appellees of their right to counsel under the Sixth Amendment by causing KPMG to place conditions on the advancement of legal fees to Defendants-Appellees, and to cap the fees and ultimately end them."
I'm not an expert on this particular area of the law, and the state action caselaw on which the court relied to get to this result is murky. But I tentatively think the court's decision is right. Constitutional rights generally (with some exceptions not applicable here) include the rights to pay for what it takes to exercise the right -- to pay for counsel, advertising space, private schooling, contraceptives, abortion, and the like. They likewise include the rights to pay for what it takes to exercise the right using money donated by friends, family, well-wishers, or others.
Thus, if the government pressures (using the threat of indictment and financial ruin) your customary benefactors to stop paying you the money you need to exercise your rights, precisely to affect your exercise of the right, that would itself presumptively violate the constitution. If the government is investigating (say) a pro-life public advocacy organization's funder for some crime, offers more lenient treatment if the funder cooperates, and tells the funder that one factor in deciding whether he's cooperating is whether he cuts off funding for the advocacy group, I think that would violate the Free Speech Clause. If the government is investigating a Planned Parenthood funder for some crime, offers more lenient treatment if the funder cooperates, and tells the funder that one factor in deciding whether he's cooperating is whether he cuts off funding that goes to paying for abortions for poor women, that would violate the Supreme-Court-recognized right to abortion. Likewise, if the government is investigating a company, offers more lenient treatment if the company cooperates, and tells the company that one factor in deciding whether it's cooperating is whether it cuts off funding for its employees' exercise of their right to hire counsel, that would violate the Sixth Amendment.
It's true that the company might well have been free to voluntarily cut off the payment for its employees' lawyers (apparently such payment was the norm at KPMG and similar companies, but probably wasn't part of any enforceable promise on KPMG's part). Likewise, the funders in the examples above might well have been free to voluntarily cut off funding for others' political advocacy, abortions, and the like. But when the government coercively pressures the funder, the government's actions may violate the funded party's constitutional rights even if purely voluntary actions on the funder's part would be entirely lawful.
In any case, that's my tentative thinking. Thanks to Paul Caron (TaxProf Blog) for the pointer.