Appellate counsel will most likely contact the appellant (defendant/criminal) at some point. It may not be immediately or as fast the defendant may like. Much of appellate work is based on the written transcripts of proceedings which the attorney will need time to review.
San Diego Criminal Defense Attorney--19 years experience. Law Offices of Jay S. Finnecy
Much of your question is Texas-specific but here is one thing I know. If the COURT appointed an attorney to serve, no action by the DEFENDANT can un-appoint the lawyer. It takes an order of the court to undo an order of the court.
Discourteous, yes. Unprofessional, yes, in the sense that a lawyer should encourage the development of a good working relationship with the client where possible. Unwise, yes. Unethical? Not clear. Contrary to law? Only if there is a statute, court rule, or court order requiring counsel to make such contact. Unconstitutional, no, unless it results in ineffective appellate representation.
The fact is, however, that an appeal is based entirely and exclusively on the record (at least in most jurisdictions) and it really does not matter very much what the client has to contribute. The briefing and presentation of the appeal should be the same whether the lawyer and the client ever have any contact or not. I do not need client contact in order to provide good appellate representation, but any lawyer with good sense and judgment, not to say basic courtesy and decency, will initiate and maintain such contact and will keep the client involved in the case.