In the 20s and 30s, a fair proportion of Heuer's range was available in either 14 or 18 carat gold. This went down a bit in the 40s, up again in the 50s, and then during the 60s there were only a couple of models at a time in gold, sometimes only one. During the pre-Chronomatic phase, those were the Carrera and Camaro; the Autavias were always in steel in this period. Gold-plating had become more popular, replacing the more costly gold-filling process and both Carrera and Camaro were also available as plated models - these are much more common than the solid gold variants.

Come the Chronomatics and the launch of the Monaco, the only model range to feature solid gold was the Carrera, with the 1158. The Autavia got a gold-plated model late in its life, and watches like the Montreal had gold-plated versions but no more 18K ones aside from the Carrera. Whether that is the vagaries of fashion, or rocketing gold prices in the 70s restricting the use to the smaller cased Carrera is open to debate.

So the short answer is, no Heuer didn't produce a gold Monaco, either solid or plated.

But the story doesn't end quite there for the Monaco. When TAG-Heuer released new versions, they did include a model in 18K:

Perhaps surprisingly, it's a somewhat handsome beast and does make me wonder what an 1138 would have looked like if Heuer had done one back in the day. I'd wager not bad.

Straying somewhat further from the classic Monaco case is the Monaco V4, available in rose gold amongst others:

If you're interested in the precious metals, I wrote a couple of articles on Calibre 11, covering the Heuer and TAG-Heuer periods:

http://www.calibre11.com/precious-metal-heuer/
http://www.calibre11.com/precious-metals-tag-heuer/