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.

My mechanic wanted to replace mine as he said the bushing were bad, but I have the type on a 94 where the ball joint is replaceable w/o needing the whole arm. I just had the bushings replaced.....they say you do need an alignment which I had done at bell tire for 45.00. That was years ago......

You'll probably need an alignment.

Beware of cheapo Chinese control arms.

MY FCP unit crashed immediately since they substituted a common soft steel
hex bolt instead of a machined and hardened pin to secure the ball joint.
The bolt deformed allowing slop at the control arm.

I'd get OEM control arms/ball joints, maybe Tasca, check with IPD.