Can a great system make a mediocre recording sound good?

All systems are imperfect.  That is they cannot perfectly reproduce the signal fed into them.  Therefore the sound that comes out will be judged either 'better' or 'worse' at reproducing that signal.  The systems that are 'better' will be improving the sound of the (poor) recording.

Therefore a system could be designed that would process poor recordings to sound like good ones.  But the changes made would render the performance different from the original recording.

A poor recording will always remain as such. What you get with a better balanced system is that even a poor recording would have a meaning. No it will not sound good but it would be easier to follow.

The better your system is, especially imaging, the more it will reveal the great, good, bad, ugly.

The more you experience excellent imaging, the more you are aware of problems.

One category is excellent but needing a slight balance tweak. I use my Chase RLC-1 for the advantage of remote balance from my listening position, in very small steps. It is amazing how much is gained from a small correction.

Another category is weirdly produced imaging, a drummer on the right moving to the center for a solo, same thing with other musicians moving about.

Get thee equipment with a mode switch for Mono.

Next we have playing Mono LP’s. Not only a true mono cartridge ignoring any vertical anything, but again, a mode switch with Mono, or sometimes better: both channels sent to only 1 speaker. That avoids your brain from it’s habit of seeking imaging when in your listening spot. You can move here and there with Mono from one speaker.

Not great music, not great engineering, oddities, BUT great songs, great memories. I keep a MM replaceable stylus cartridge just to play them with, to enjoy as I always did, but not gonna wear out my expensive MC non-replaceable stylus for them.

I often say "I can't hear any difference", but I certainly can hear differences when they are there to hear.

If a high end system is better at at processing the signal ( reducing EMI, RFI etc.) wouldn’t that give a  bad recording the impression of sounding better at least in some aspects? 

My current house of stereo system makes every record sound better. Whether they are well or poorly engineered/mastered. Across the board, all sound better than they did with my older systems in various rooms. I must have done something right this time with both the system and its acoustic setting. But, however a poorly recorded album's sound improves, it still basically sucks 😜