will doing a really hard upper body workout affect running performance in the following days?

You use your arms to run too. Plus, resistance training fatigues the central nervous system, which will ultimately affect your running, even if you only train the upper body.

If you are used to it and you keep it under control, it could actually help you by giving a global testosterone and growth hormone release which will help your legs also. If it is too heavy than that is another story.