You surely can, but it could be very difficult. Publishing research without any affiliation could be difficult because of various reasons beyond your control.

You surely can, but it could be very difficult. Publishing research without any affiliation could be difficult because of various reasons beyond your control. Having an advisor or a team can significantly boost your publication quality. Think in terms of how quickly you can validate your ideas, get proper feedback while preparing the publication, and get proper visibility for your work. Keep in mind that several large tech-companies (e.g., Google, Facebook, Yahoo, IBM, Xerox, etc.) look for research engineers, or software engineers that work with research teams. You could start looking for such jobs and collaborate with teams/team members that publish their work at top journals/conferences. Such teams tend to be highly selective, but that is definitely something different from taking competitive exams. You'll probably have to create a strong portfolio to indicate that you can "independently" conduct research (e.g., showcasing some novel ideas on your website, sharing implementations on GitHub, listing your contributions to open-source projects, etc.). Another option is to look for any research associate positions with labs/professors.