If I drink a strength potion does it deal more damage against the ender dragon?

Yes, strength potions increase the damage you inflict to the dragon, but only for your sword attacks, not with the bow.

There is a tutorial on the Minecraft wiki on how to defeat the dragon, and it includes a section about useful potions.

I defeated the dragon recently, and the only potions I took were strength II, and a couple of instant healths. But I already had an elytra and a lot of rockets, otherwise it would have been much harder.

Good luck!