No, recompressing a save has no measurable difference to performance.
Factorio saves produced by the game are optmized for speed, not size. While this does allow for a quicker return to gameplay, it is not the most optimal for sharing maps between people.
Fortunately Factorio is capable of loading and running zip files compressed with more agressive settings. However, before we go ahead and start recompressing saves, we should verify that there is no performance difference to doing so. It's unlikely that there would be a performance change, therefore this test is a case of 'trust but verify'.
For this test we will take a save, unzip it, and then rezip it with more aggressive settings. While the zip format allows for additional algorithms, like bzip2, only deflate is acutally loadable by Factorio. It is for this reason that we will compare zips compressed by Factorio and those compressed via deflate.
Our test setup will consist of around 9k furnaces fed by and feeding to infinity chests. Additionally, an area of 2k x 2k was generated with normal (minus water) terrain. Pollution was disabled as per usual.
This resulted in a filesize of 7.5MB for the Factorio produced zip, and recompression brought that figure down to 6.6MB.
Tests were conducted using the --benchmark-verbose command line flag, running for 260 ticks, and 100 runs. The best ticks of each run was taken (ie: fastest tick of tick 0, fastest tick 1...).
Collectively, the normal Factorio produced zip measured 0.3% slower than the recompressed version. Since we only did 100 runs, this value is definitely within margin of error. We would need an excessive number of runs to be able to conclude one is slower than another.
This result was exactly the result we expected. That said, without data nothing should be assumed.