Does Strength affect the Ender dragon in Minecraft [duplicate]

No, potion effects from potions will not be applied to both the Enderdragon and the Wither.

The dragon does not make use of the generic.attackDamage attribute, which means Strength would not work even if it could be applied. The Wither does make use of that attribute, but effects are still not applied to it.

As an in-game example using a Wither, the following applies the Strength effect to it:

/summon WitherBoss ~ ~1 ~ {NoAI:1b}
/effect @e[type=WitherBoss] minecraft:strength

And the following will display all data on the Wither, showing both the lack of an attackDamage modifier as well as the ActiveEffects list, despite the above /effect command stating it was successful:

/entitydata @e[type=WitherBoss,c=1] {}