No they didn't. All GT convertibles had buttons on both sides, but where the ones on the left on the coupe did the bluetooth controls, on the convertible they only did the radio as BT wasn't available as an option.
If it doesn't have buttons on both sides of the wheel then it's not a GT car UNLESS the wheel has been replaced at some point, although why you'd do that is a different kettle of fish.
Oops my bad
When I was searching for 350z's, all the 'GT' convertibles I looked at only had one set of buttons on the steering wheel also so I thought that was the way they were meant to be. Luckily I didn't buy one then!
I've just researched this and looked at several photos of GT convertibles. It would seem that the extra buttons were introduced with the facelift model in 2006. I've looked at a few roadsters from 2005 advertised as "GT" and they are all missing 3 buttons from the steering wheel but they have all the other things that GT's have (Bose, Leather, Heated Seats). If someone can produce a photo of a pre facelift roadster with 6 buttons then I'm obviously wrong
Pete
You are correct. Buttons on both sides from MY06 onwards only.