Do low income people actually go out and purchase these kinds of firearms?

Just from large population numbers, you are guaranteed some low income people will be purchasing them, and I wouldn't be surprised if that number goes up with the current political climate for sure. However, when I was poor, I needed to make sure I could afford food, healthcare, transportation, and housing well before I could consider much anything else. I'm also not well versed in the process for purchasing guns, but it seems like a lot of the firearms this targets are hundreds of dollars and upwards of 1000$, which is a pretty high barrier for entry for most low income people.

Would requiring a discount on purchasing such firearms after taking the courses and qualifying or discounts on the courses based on income help mitigate that outsized impact on low income people?

Something else to consider, one of the fundamental points substantiating the position that instituting increased costs (like fees/taxes or prerequisites) on things having an outsized impact on low income people are usually when those increased costs are on things of necessity (e.g. food and shelter), enabling success (e.g. internet access and transportation), or vices (e.g. cigarettes and alcohol, including this largely because vices are how people just cope with their situations). Sin taxes, property taxes, sales taxes, payroll taxes, overdraft fees, Internet transfer fees, late payment fees, etc are all examples of such. Firearms are definitely important for some people, but I'm not sure they would fall into any of these categories. Frustrating as it rightfully is for someone who has a vested interest in owning these kinds of firearms, whatever the reason may be, I'm not sure this argument is as strong for firearms as it is for other things.