Sounds difficult. Both, cpu and gpu, are weak for actual streaming (at least actual expectations). So can "it" stream is a weak question.
Playing on PS4 sounds good in a first manner, cause the PS4 has the heavy load of rendering the gaming itself. Your PC would "only" have to grab, encode and send the video and audio content. But this could be enough to outreach and overload your system.
The demands on calculation depend alot from your expectations on resolution, framerate aso. Your system will be at least on an "edge to no-go". So don't have too much expectations. Just give it a try, but keep calm if it fails for your needs.