Yes, if done according to the law. (Richard Nixon was certainly impeachable, and would have been impeached had he not resigned; the articles of impeachment were drawn up and voted by the House Judiciary Committee.)
Here’s the analysis in the case of the removal from office of the former Honduran president José Manuel Zelaya Rosales, prepared by the Directorate of Legal Research of the U.S. Library of Congress:
V. Was the removal of Honduran President Zelaya legal, in accordance with Honduran constitutional and statutory law?
Available sources indicate that the judicial and legislative branches applied constitutional and statutory law in the case against President Zelaya in a manner that was judged by the Honduran authorities from both branches of the government to be in accordance with the Honduran legal system.
However, removal of President Zelaya from the country by the military is in direct violation of the Article 102 of the Constitution, and apparently this action is currently under investigation by the Honduran authorities.
Hat tip: Daniil Gorbatenko