Minecraft baby zombie riding a zombie villager

No, they cannot.

This is because they have a different AI behavior than a grown up Villager. This is also the reason why you can't trade with baby Villagers.

However, if you have the patience to wait for 20 minutes or so, they'll grow up and they will be able to farm and trade.

Unfortunately the pocket edition is notorious for friendly NPCs and pets disappearing when spawned by the player. It used to be an issue with my dog Nigel and his pups in the game.

Frequent visits apparently help, but sometimes it simply isn’t worth the watch in the pocket editions. :/