not sure it directly benefits the root growth, but for overall plant health, it is definitely a well known source of N and K fertilizer
(potassium nitrate= potassium & nitrogen)
there is a belief that both N & K in potassium nitrate mutually help each other with absorption by root systems due to their +/- charged ions keeping them available in the soil (less likely to get locked out)

anyway, I've used Saltpeter (form of potassium nitrate) for soil applied fertilizer, diluted half strength for outdoor plant beds with great results in the past. highly water soluble, so very promising for foliar application if you wish, but have not used directly on leaves myself.

I can only suggest a test run to see if it benefits leaf rooting or not. Although I'd be interested in the results/conclusions

I will do some research into concentrations. I could take two leaves from the same plant and treat one with the concentrate. Certainly wouldn't be enough to be a very scientific test (too few subjects, too many variables) but it would be interesting to see if there was any appreciable difference.
I am starting a tray of seedlings so I have plants to perform experiments. Test Subjects.
I am turning into the mad scientist. As I said before, when I had fish tanks a friend of mine asked me "When are you going to stop torturing those poor fish?" Now it is "When am I going to stop torturing those poor plants?"

Good luck, Lucky.

I hope you'll post progress pictures!

OK
Anyone want to experiment, I found a website that states 1 tbsp.salt peter per gallon of water.
That is for orchids. The orchid growers seem to use potassium nitrate for rooting and as a part of homemade fertilizer.
I would dilute it a bit possibly.
Salt Peter is available at drug stores or so I am told.