Did Cherner actually design this?  

No pic
No pic woody.

It is slow to load...
Possibly a bandwith issue

Doesnt feel right
This chair doesnt feel right...just not elegant or flamboyant enough to be a real-deal Cherner. It feels a little like the waist is too fat, and the flare at the top isnt dramatic enough. And the legs are too spidery with their curve...
If i had to guess I would say it was a Plycraft-like company stealing the design and making a few changes... see the white chair below.

I like that lamp in the...
I like that lamp in the picture with the white chair is that a item I can buy at a store currently

My opinion
I believe it is a Plycraft chair... although I can't find one with a label at the moment. They pop up on eBay about as often as the typical Cherner chairs. I think Mr. "Bernardo" / Goldman probably altered Cherner's design. Perhaps the "neck" was widened to reduce breakage problems.

But why
But why change the bend in the legs then? Or the lower swooping of the arms. Who else worked with plywood at the same time as Plycraft? Selig? Charlton? I would pin it on them before Plycraft - despite all the legal issues Plycraft produced the Cherner chair until the mid nineties.

Well...
These are labeled Plycraft:

Also,
The white chair you posted is different from the one I posted. The back is different and the legs are even more curved.

Well damn
Plycraft is such an odd company. The more I think about it they did do a million different copies of the Eames... I guess that brings us full circle to your original question as to whether Cherner had any involvement.

Cherner and the confusion about the Cherner Chair
Cherner didn't design the Cherner Chair, it was designed by Paul Goldman the owner of Plycraft. While I agree Plycraft ripped off many things, they also had some great designers. I mean hell, Mulhauser designed the Coconut Chair. If that ain't talent I don't know what is?

Goldman did not design the...
Goldman did not design the Cherner chair-Cherner did. Goldman tried to rip Cherner off and attributed the chair to the mythical "Bernardo". See below from Modernism Magazine:
it was created in 1958 by the American designer, Norman Cherner. Commissioned by Paul Goldman, the previous year, Goldman's company, Plycraft, had been engaged to make George Nelson's loop-backed Pretzel Chair for Herman Miller. Sadly, this charming- but-costly chair was discontinued and Goldman was left holding the expensive tooling. On Nelson's recommendation, Cherner was asked to design a similar chair using the same machinery.Cherner signed a contract and delivered his designs, only to be told that the project was off. A few months later, he was dismayed to discover his chair for sale in New York. According to the label it was made by Plycraft and designed Bernardo.
In 1961 Cherner took >Plycraft to court, where Goldman admitted his deception Bernardo was apparently a figment of his publicity team's imagination. Still, designer royalty battles not being big news, few people noticed and for years Goldman himself (who died this year) was spuriously credited with the chair's design. "

Thanks jesgord
For the clarification... I meant Goldman / "Bernardo" rather than Mulhauser, in my previous posts.

Cherner / Plycraft relationship . . . Who is Lou App vis-a-vis the Cherner armchair?
I have a set of two "Cherner" armchairs that look exactly like the ones here except they have black leather seats and backrests and have the label "Lou App designer for Plycraft 1985." Can anyone let me know if they've heard of the Lou App version and whether these chairs might be worth something?

I guess
Lou App was a later designer for Plycraft, and he took Cherner's design and modified it. I guess they are worth something because many people probably assume they are Cherner. There is a set of six armchairs on 1stdibs listed at $2400... But you know how 1stdibs goes.
This design sells regularly on eBay for about the same as or a bit less than the original Cherner design... Again, I think the selling price is partly due to confusion about the designer. Designer name aside, these chairs are not nearly as refined as Cherner's, but perhaps they are less prone to cracking.