So the real answer is no but yes sort of kinda but not really but sure it does.
So the plants root mass grows more or less vigorously based on a number of factors. There are lots that can be done to impact and cause the roots to grow faster.
The lights and your choice of grow method impact the vigor and health of the plant. So if the plant is stalling and stunted or if the plant is thriving and expanding the growth then the roots will vary with that in most cases.
There are many lighting techniques and lots of reasons for doing 24 on or 18 on or gas lantern routine. There is a lot to learn about light my friend... but if you think you can grow faster with 20 on vs something else on then you may cause faster root growth sort of inadvertently.
I think of it more as we are not perfect and can run them very close to perfect and the fewer stresses and mistakes we make the close to ideal potency and yield we can achieve. So minimize mistakes. In doing so you will increase the root mass faster.
All that said...Light in general is not considered associated at all with root mass growth. The roots grow as fast as the plant needs them too.
The way you make roots grow faster is you make them incapable of supplying the needs temporarily so they grow searching for more. that is done ideally by drying out the medium.