I did some testing with true synth races and found that they just don't manufacture population like they should, even when the world is just doing the economic stimulus on repeat. I checked and they do have the resources, they just aren't building the pops.. For a while I thought they weren't invading core worlds, but after a while of forcing them with the Everwar challenge, the Grey Goo (synthetic Mimots) did start invading, so, the lack of manufacturing population is hurting their ability to compete with regular races. Also, in the savegame, the borders had been pretty much stable for hundreds of turns and the Grey Goo have the capability to conquer the heck out of things, but they don't.

https://www.dropbox.com/s/f0ijkj00kcmzi18/synth%20everwar%20test%20turn%200.GC4Sav?dl=0

I also did a test with a synthetic trait race and an organic pop (anybody besides Yor) and it turns out that they can 'build' pops in addition to the normal growth rate (though inability to build farms is gonna hurt), maybe that should be renamed 'cloning' or something when it comes to organic pops with the synthetic civ trait?

Also, on one run when I accidentially left one civ with an organic pop, they somehow managed to make enough food to not end up with populations starving.