Have any designers been exceptional inventors?  

Yes DC...
the Raymond Loewy bus is a design patent and as such does not qualify as an invention.
I will try to find a picture of the Henry Klein "egg" chair...it is much much much closer to the Arne Jacobsen one.

Design Patent
DC: Yes, it's a design patent -- one of a number of bus designs that Loewy did for Greyhound in the early 1940s.

I'm bored
Not all inventors but...
http://en.wikipedia.org/wiki/Fran%C3%A7ois_Hennebique
http://en.wikipedia.org/wiki/Isambard_Kingdom_Brunel
http://en.wikipedia.org/wiki/Joseph_Paxton
http://en.wikipedia.org/wiki/Pier_Luigi_Nervi
http://en.wikipedia.org/wiki/Gustave_Eiffel
http://en.wikipedia.org/wiki/Robert_Maillart
And there was I think an East German who developed the spraying of very thin concrete shells for things like concert halls and grain silos, quite egg shaped and proportionally thinner than egg shells, I'm sure Koen would know his name.