Rik Mayall as Peeves the Poltergeist (Harry Potter and the Philosopher's Stone)

I've done some research on this, and I've come to some conclusions.

1. Peeves was meant to be a CGI character, with Rik providing his voice. However, Rik was indeed on-set and was doing what may have been some motion-capture for the role akin to Andy Serkis in the Lord of the Rings trilogy, but nonetheless all signs point to Rik having done on-camera work for the movie.

2. The kid actors laughing at Rik's performance wasn't a deal-breaker as many may believe. In the famous interview with Rik on his deleted role, he mentions being told they'll "do the voice with someone else." Now, at this time, Rik was still in the film and would be for an additional three weeks before the production made their decision. Factoring this with Peeves being a CGI character, I can assume they meant they would have a stand-in do the performance for the need to get proper filming done and have Rik record his voice in post-production (we have no knowledge of Rik coming in to record lines, but he may very well have since Columbus was at one point considering adding Peeves into the film via DVD extras, it is unknown).

3. Despite this, it is all but confirmed Rik was indeed filmed on-set reading his lines. It's just if released it would just be Rik giving his lines, to an audience of kid actors in hysterics, possibly rending some of his lines inaudible. I'd pay to see that, of course, but Warner Bros. possibly didn't see the quality as fit to release as a result, or were waiting for Columbus to decide on making those Peeves scenes.

4. Here'es a small bit on Columbus discussing Rik and his cut role as Peeves: https://ew.com/movies/harry-potter-concept-art-never-made-the-movies/

5. If you were wondering what Peeves's scene may have entailed, it apparently involved him flying around and setting some broomsticks on go: http://www.bbc.co.uk/gloucestershire/focus/2003/08/potter_more_info.shtml