Wow. This is a very creative question with some amazing insights into why the human heart, and all other mammals, is designed to include the right atrium.
To answer this question simply, no, humans cannot survive without the right atrium of the heart. Clinically, there are no reported cases of humans surviving without an intact right atrium. In fact, there are many diseases related to dysfunction in the right atrium's structure, blood supply, or electrical capacity.
Frogs and other lizards don't necessarily have a missing right atrium, but instead they have both a right and left 'atrium', known as auricles, and one ventricle. Humans, along with other mammals, also have auricles on top of both atria which can be considered a vestigial structure, yet still has function. Auricles simply allow for more blood collection, or housing, as a way to supply blood to the heart itself.
Other important reasons to consider why humans cannot survive without a right atrium are the following. First, the right atrium does not have a valve which allows passive flow of venous blood to pour into the atrium upon diastole, or the relaxation cycle of the heart. Second, the pacemaking sites are located in the right atrium which begins the electrical cycle of the heart beat. Third, the very important coronary vessels circle around the right atrium as a means to provide blood supply directly to the heart.
Without the right atrium, all of the associated functions and structures would have to be replaced, or re-positioned, to another location. In that event, even the new sites (ex. left ventricle or left atrium) would have to be changed in some facet in order to make up for the function of the right atrium.
Hope that helps!