Should animals despawn in Minecraft on Xbox One if i put them in a Mine cart and send them down?

So I believe they should be able to get a fair distance, but since they can't move, should they be able to despawn? I trapped a bunch of animals and tried to move them via minecart, and a fairly far distance off, there were just empty minecarts inbetween my power rails, like they despawned and stopped the carts? Even though they can't move ANY blocks in the minecart, they disappeared? So any advice on moving the animals? I built a path but it takes a while luring them with crops because they move so slow

Also, the distance I'm trying to move them is at least 100+ blocks. From a far forest, to my homeland. So am I just going to have to lure them? Because I guess I could just put unpowered rails about where they despawned, and walk over there and power them, like, make minecart stops in between the distance, but I'd rather just walk with them then.

Just lead them there with some wheat - just set game to peaceful to ensure you're aren't griefed by a mob.