Former goldsmith here. I used to work with gold, a lot, but not so much with steel, and I never did damascus or mokume gane. From your question I'm guessing it may be the opposite for you ?
Before thinking about durability, I would question feasability. Due to their very different fusion temperatures, and different "behavior" when heated, these two metals may be difficult to mix together.
To illustrate this, you usually work gold while it's cold. If you try to hit or bend it while it's red, it will offer almost no resistance. Meanwhile, steel offers quite a good resistance even when it's red hot. How do you forge those two metals together in these conditions ?
But again I am no expert in forging, even less in damascus or mokume gane.
I can only tell you the metals commonly used together are :
- silver/gold/copper for mokume gane.
- steel/other steel for damascus.
About the durability, I think, if you manage somehow to make your ring, it would be quite a durable ring, because the steel would prevent rose gold (which is already one of the hardest of golds) to suffer too much from abrasion. The only concern that I see may be the need to change the ring's size (quite frequent after 10+ years).
Other than that, such a ring should last for a lifetime and more, assuming you treat it with care (=> taking it off when doing something that could damage it).
Quick note, just a basic reminder on how to keep your jewelry as long as possible :
- Don't make any part of the ring thinier than 1.5mm.
- Don't wear it in bed. Bedsheet are quite abrasive over time.
- Don't wear it into the shower. Since I assume we're talking about stainless steel, this is not so much about durability than about the risk of loosing it into the siphon.