A paper in UG will have a huge impact on your application but it is not required by any means. Speaking with EE terms, you should be note that there are a lot of "non-linear" effects in the application processes. So, you can not be sure that whether the lack of something will effect your application as well as being 4.00 will guarantee your admission.
However, talking from experience I think that having a GPA over 3.9, having done UG research, and applying to the areas similar to the UG research topic, and having 1 or 2 "research LOR" (as opposed to "course LOR" ) should ensure you admission of at least 1/3 (among Stanford,MIT and Berkeley). 4.00 GPA might bring you 2/3. but 3/3 if a little bit of dream
ps: I can recommend you to stress your research in your statement of purpose as much as possible.