If you're more than 32 blocks a way, they have a chance to despawn as a result of that. (Check the 32 blocks, but it's something to that effect)
If it is a tier 5 spawner from a shard then yes. I know from a bad experience I had that I had involving a quarry turtle. I set the turtle up to take out a chunk right next to my enderman tier 5 spawner. My wireless transmitter that kept the machine off was in the chunk I told the turtle to take out. Man the lag was horrible (about .1 FPS). Well over 1000 entities. Dispite the lag, I was able to setup a new wireless transmitter to shut it off. Then I spent the next 1/2 hour killing off the enderman. I hadn't finished the farm yet. Just set them up for enough fall damage to do one punch kills.
So if i set up mfr grinder to kill those mobs. It will still working right? And it is the same with auto spawner?