Mobs immediately despawn if closest player to them is farther than 128 blocks. Soul shards don't override this behavior of mobs. They spawn mobs when they should despawn, you can test it by enabling entity radar in REI's options. If you place a spawner and fly up more than 128 blocks from it, you can see that red dots representing mobs will appear and immediately disappear.
I didn't test it, but you can try placing your spawner in a dimension without any players. If spawner works in that conditions, mobs shouldn't despawn.
rei's test is useless, for 2 reasons:
1- rei's minimap only have access to client-data, not server data. Hence, if the server dont send mobs to client, rei's minimap cant draw them.
2- server's have a limitation range to send entities to clients. The same way if you are in the nether the server is not sending to your client overworld related data, its the same with entities too far from you. The client beeing unable to see them NOT EQUAL mobs doesnt exists.
And, for the red dots disappearing, if your limit is 128, what happen if enemies spawn at 127 and fall to 129?