Popping noise after suspension rebuild

Yes. No.

In that order.

Whatever triple RRR said, I'll agree with him on principle, but to elaborate...

You shouldn't have any noise coming from a properly installed front-end.

If you loosen up your control arms a bit and drive the car to eliminate a bind, and then have the alignment re-done, if you keep the mileage under a couple hundred or so, you won't do any lasting damage to the tires or suspension components.

Keep in mind that most alignment shops have zero clue what to do with our cars... Never mind the bias-ply vs radials debate... so learning how align your car and investing in the right tools to do so (tape measure, angle finder, etc.) is well worth it.