The sixth amendment gives you the right to retain counsel, so if you have the monies to pay for counsel, then no one can interfere with that right.  The right to counsel is generally regarded as a constituent of the right to a fair trial.

“Nevertheless, where the right to be assisted by counsel of one’s choice is wrongly denied, a Sixth Amendment violation occurs regardless of whether the alternate counsel retained was effective”.

Kaley v. United States

134 S. Ct. 1090 (2014)   Cited 248 times   13 Legal Analyses

Describing the “vital interest at stake” in “the constitutional right to retain counsel of their own choosing,” as described in Gonzalez-Lopez, 548 U.S. at 146-48,150, and explaining that, “having the ability to retain the counsel [they] believe to be best – and who might in fact be superior to any existing alternatives – matters profoundly”

Rivera v. Marcus

• • personState, Provincial or Regional Government
  • personGovernment

Holding that Plaintiff, who provided foster care for her half brother and sister, had liberty interest in preserving familial relationship and that termination of foster care agreement with state—without any notice of reasons for termination or any opportunity to retain counsel or be heard in subsequent proceedings—violated her rights to procedural due process

U.S.
v.
Gonzalez-Lopez

In sum, the right at stake here is the right to counsel of choice, not the right to a fair trial; and that right was violated because the deprivation of counsel was erroneous. No additional showing of prejudice is required to make the violation “complete.”