In noncriminal matters such as deportations, there's no right to counsel at public expense. The broader rights to due process of law and habeas corpus have generally been held by the courts to apply to immigration detention and deportation, and people are certainly free to hire counsel at their own expense in such proceedings.

It gets tricky when a deportation is completed before a court can hear the case. Attempting to prevent a detainee from communicating their location and situation to someone who could bring a legal action on their behalf doesn't appear to be explicitly illegal, but it's certainly an attempt to subvert due process and probably ought to be illegal.