I say yes you should, but I am more of a stickler for a centered pattern than some people are. The improved cylinder pattern will be wider than the turkey choke pattern, so it will be more forgiving if it is not centering well. So, it is less of a factor, but still significant in my opinion.
Your IC pattern could be 4 inches low at 40 yards and you won't know it unless you shoot it and see. Will 4 inches make you miss? Probably not often, but it could make you miss occasionally. I've seen guns that were 16 inches off. Will that make you miss? Probably more often than you would guess.
I've also seen chokes that were accidentally threaded a little off center, causing a gun to shoot left, right, high or low.... I personally would want to know that if it was happening to me. I might just go get another choke and my problem is cured that easily. But, I won't know to do that unless I pattern my gun.
Even the threading in the gun barrel can be off. One company (Briley in Texas) offers a service where they pattern guns like that and make "eccentric chokes" for just that gun to get it to shooting straight. Briley is a class act in my opinion.
You will often hear the saying that you point a shotgun rather than aim it like a rifle. In some cases I partially agree with that. With a fast shot (like a rising quail going into brush) you probably do more pointing than aiming, because of how fast everything happens. That's why the cast of the stock and drop (to fit the shooter) is so important for a gun like that.
With trap guns, the stocks are straight so that your cheek doesn't come down so low and therefore makes you shoot high, which is good, because the clay bird is rising. It is designed to be that way.
Bottom line for me is: I want to know where my gun is hitting. I may or may not do anything with sights to correct it, but I may aim a little different to compensate for it. If I'm pass shooting at a dove with that high shooting trap gun, I may decide to aim a little low so that I will center my pattern.
I don't like missing...and I sure don't want to miss because I don't know where my gun is hitting....
If you've never missed a shot, just ignore everything I said, don't pattern the gun and keep shooting....