Hello Manuel,
We (Uni Bern) are running 4 web servers with ILIAS 5.1.17 (php5) with mpm-prefork and added a 5th web server with identical specs but with php-fpm. There were no problems adding a new web server with a different php process manager. They all work along pretty well.
Performance:
No performance gain was noticed so far. AB (https://httpd.apache.org/docs/2.4/programs/ab.html) shows around 15% slower performance for the server with php-fpm for retrieving a landing page anonymously (ilias.php?baseClass=ilrepositorygui). The only difference seen so far is that php-fpm is much better on physical memory, as expected, leaving more of the RAM to caching data which in turn might increase overall performance. As you can see here, the left web server with fpm actively uses 830MB while caching the remaining 15+GB, whereas on the right side mpm-prefork actively uses 1600MB while having lower load for every measured interval!! and having only 14+GB for caching left. For web servers with 4GB RAM that would be a huge difference, and fpm should be considered.
Since the php interpreter doesn't get faster with php-fpm, the huge gains other websites report are probably due to other configuration issues (like constantly creating new processes or swapping, but I am only guessing).
Check this small conversation for similar results: https://www.reddit.com/r/PHP/comments/4bi9a4/why_is_mod_php_faster_than_phpfpm/?st=j2fxg1ac&sh=39003363
I guess there are no real shortcomings in changing to fpm and especially if the actively used RAM space is bigger (depicted by the green vertical lines).
Best,
Tomasz