No. Although, it would be interesting to see if you renounced your citizenship at your home embassy and then were placed in removal proceedings, what effect that would have. Most likely, the government would determine your renunciation was not effective and send you home. It would be an interesting case.
Renunciation of citizenship must be done prior to an immigration event, for renunciation to have any effect. For example, you must renounce your native citizenship prior to illegally entering the US. Otherwise, even if you later renounce your foreign citizenship, the illegal immigration event (entry without inspection, for example), occurred when you were a foreign citizen, so you will be deemed a citizen of the country from where you came. Designation of a country of deportation is regulated under 18 USC §1231(b). (b)(1) controls arriving aliens; (b)(2) controls all other aliens. Specifically, the order of priority for deportation is as follows (18 USC §1231(b)(1)(C) and 18 USC §1231(b)(2)(E) — (E) is used here, as it encompasses all conceivable legal scenarios):
(i) The country from which the alien was admitted to the United States.
(ii) The country in which is located the foreign port from which the alien left for the United States or for a foreign territory contiguous to the United States.
(iii) A country in which the alien resided before the alien entered the country from which the alien entered the United States. (iv) The country in which the alien was born.
(v) The country that had sovereignty over the alien’s birthplace when the alien was born.
(vi) The country in which the alien’s birthplace is located when the alien is ordered removed.
(vii) If impracticable, inadvisable, or impossible to remove the alien to each country described in a previous clause of this subparagraph, another country whose government will accept the alien into that country.
There are certain countries were deportation is not practical or possible. For example, Sudan, individuals who arrived from Vietnam before 1995, etc. In those specialized cases, you need to contact us immediately, as certain procedures must be followed to ensure you are not sent home regardless of treaty regulations.
Generally, as a matter of best practice, you do not want to designate a removal country in Immigration Court, as it may limit options under (b)(1)(C) and/or (b)(2)(E) above.