I have not found a clear yes or no answer but my opinion is No. The prisoner and the attorney have the right to speak with each other. The prison is interfering with the right to counsel by preventing the lawyers from meeting their clients. And interfering with the rights of the lawyers to practice their profession.
See Keker v. Procunier, 398 F.Supp. 756.
Attorneys brought civil rights action against officials of state correctional system alleging that certain prison practices interfered with their right to practice their profession. On defendants' motion to dismiss, the District Court
, MacBride, Chief Judge, held that prison practices requiring attorneys to meet with their client in hot interview room separated by a glass partition, communicate via telephone and be subject to continual surveillance by guard constituted an interference with their right to practice their profession; that attorneys had standing to allege that such practices violated their client's Sixth Amendment right; that such practices did not constitute cruel and unusual punishment
; and that complaint
which alleged that acts of state officials were malicious, intentional and deliberate was sufficient to state claim for punitive damages.
The prison can make reasonable rules for security, but cannot punish inmates by depriving them of the right to meet their attorneys. Obviously no visits would be allowed during a prison riot.
I hope this information is helpful.