The answer to your "is that roughly right?" question is: yes, roughly.
You're essentially asking for a relationship between watts/kg and VAM (velocità ascensionale media, a term coined by Michele Ferrari the famous (or infamous) Italian physician and cycling coach). VAM is the gain in elevation (in meters) one could achieve in an hour for a given power and constant slope. Ferrari noted that a pro rider producing about 6 watts/kg would have a VAM of around 1600.
Here is a graphic that shows how many meters a rider producing 175, 200, and 225 watts with a total mass (rider + bike) of 85 kg could expect to climb in one hour at various gradients. This graphic takes into account rolling and aerodynamic resistance, but at steep slopes the amount of power allocated to these are small and the amount of power allocated to climbing dominates.
![VAM at various powers for a total mass of 85kg](https://cdn.statically.io/img/i.sstatic.net/04Knw.png)
Although VAM doesn't have a true asymptote, you can see from the graph a key characteristic of VAM: that as the slope steepens, the change in VAM decreases. This is the basis for the approximation that "maximal" VAM doesn't depend very much on the slope: once the slope becomes steep, VAM doesn't change much.
Not obvious in this graph, but often helpful to know, at the far right edge (i.e., for steep slopes), the difference in VAM between the various powers is almost proportional to the difference in power: that is, a x% difference in power will translate to almost exactly a x% difference in VAM. That's because at steep slopes your speed is low and when your speed is low the aerodynamic component of power (which varies with the cube of speed) becomes less important and is dominated by the power used to climb (which varies linearly with speed). The slower you go, the more closely power and speed are linearly related. Thus, if your target were 200 watts but you could only average 180, VAM would be very nearly 180/200 = 90% of the VAM at 200 watts. If you could produce 210 watts, VAM would be very nearly 5% more.
You did not ask this but sometimes you will want to know the slope or gradient for a particular power and speed. A rough rule of thumb for the slope or gradient is to take your watts/kg at that moment, divide by your speed in km/h, then divide again by 3. The underlying reason for this rule of thumb can be found in this bicycles.stackexchange answer. In that instance, the question was about finding the power for a particular speed and gradient; in the instance here, you're just solving backward given speed and power to find gradient. For example, if you were riding at 200 watts, your total mass were 85 kg, and your speed were 10 km/h, the rule of thumb would produce an estimate of the slope of 0.08, or 8%.