Can you still get and use Auriel's bow when you join the Dawn Guard?

The bow itself doesn't change, so yes, you can use it. It's still a powerful sun-damage weapon. What changes is whether or not you use your companion's blood to make the arrows that blot out the sun.

Bethesda games often have their story splits early for achievement purposes, but if you're achievement farming, the best choice is to make a hard save right before a point of no return on the decision. Then you can play through each branch, make a hard save at the end of that branch, reload the first save, and once you've obtained all of the achievements, load and keep the branch with the outcome you wanted.