I don't think anyone should equivocate on this question . . .

Any part replacement that establishes suspension geometry SHOULD be followed-up with an alignment.

Is it possible that you can replace a suspension-critical component and not require an alignment?

Of course!

And, occasionally, people live to 95 smoking three packs a day.

Does the control arm establish suspension geometry? Yes.

You may forego the alignment and find the car appears to drive straight and think to yourself 'see, I didn't need an alignment.' But 20,000 miles from now, when those 50,000-mile tires have scraped themselves clean, you'll learn that the extra $50 or $100 spent now was worth it.