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Not that I've seen
I have never seen that particular configuration, and I don't know that it would be a good way to use a wire side chair. The stress of tilting back in the chair might prove to be too much for the wires and electronic welds. You may well end up damaging the wire seat.

Pegboard
That was actually one of my concerns at first. But the more I think about it - wouldn't the chair be subject to more stress on a non-tilt base? Won't the tilt give some relief to the stress as the sitter leans back?
My dilemma is twofold.
One - I kinda really need to have a recline for my desk chair. (altho I do think the non-tilt base is better proportioned for the chair)
Two - I have both a spare wire shell and a spare roll/tilt contract base.
I'll probably marry the two and see what happens. It is a tiny bit worrisome, though, that the chair doesn't appear on EamesOffice.com.

I would agree...
Although I didn't major in engineering or physics, so take this with a grain of salt...
But I would think the tilt position would put more stress on the mount points, particularly the front two. The weight on the deep part of the seat would alleviate some of the pressure to the back two. But as you lean back, you would really be pulling against the front screws.
Also, your point about Herman Miller apparently not offering it is a solid one.

Safety or aesthetics
I wonder if it might be a safety or aesthetic issue having side-shells on a tilt base. It seems all the side shells - plastic and wire - were fitted on a narrower contract base (PKC, PSC, PSCA etc) which does look proportionally better to the shell. The wider tilt base was fitted with the arm shells (DAT)
Perusing Eames Office and Google images there are no examples of any side shells on a tilt pedestal base, with the exception of the much taller drafting table base (and one in a vintage shop that looks married).
Maybe it wasn't done because it just...wasn't done.
http://eamesdesigns.com/?s=PSC

Does anyone really
put a tilt base on an armless chair ? Isn't it a part of the comfort -- even the operation -- of a tilting chair, that one has a place for one's arms ?
How many armless tilt chairs can one name ?
The arms of a shell -- the side panels -- would take some of the stresses, the live loads, of tilting, wouldn't they . . .