Resolution: Invalid

Reproduction:

• Go to the End.
• Obtain both healing and harming arrows* and a bow (or crossbow).
• Try to aim and shoot the Ender Dragon.
• See results.

*Use 

/give @s tipped_arrow{custom_potion_effects:[{id:instant_health,duration:20,amplifier:5}]}

and

/give @s tipped_arrow{custom_potion_effects:[{id:instant_damage,duration:20,amplifier:5}]

to have larger damage effect.

Result:

The Ender Dragon takes damage on both types of arrows.

Expected:

The Ender Dragon should be either normal or undead which means only one type of arrow will damage it.

Resolution:

I realized the large amounts of damage I was inflicting on my end were from the over-enchanted crossbow I used to test and as explained by Dhranios, bosses are immune to status effects.