Non-boss mobs that naturally regenerate health like all sub-classes of horses (Horse, Camel, Llama etc.) and the Allay continue to do so when their NoAI flag is set to true.

This behavior is inconsistent with that of the Wither, which does not regenerate health when {NoAI:1b}.

To reproduce:

1. /summon minecraft:horse ~ ~ ~ {NoAI:1b,Health:0.5f} 

1. /summon minecraft:wither ~ ~ ~ {NoAI:1b,Health:0.5f} 

1. /tick rate 200 

1. /data get entity @e[type=minecraft:wither,limit=1] Health
   /data get entity @e[type=minecraft:horse,limit=1] Health
   

Observe that the health of the horse continues to increase, while that of the wither does not.