I think inviting anyone to play whatever they want (so long as it's acoustic) will really work.

I think it probably will - my local FC, which has just this policy, has grown over the years from "six local performers with an average age of 40 do two in the first half and one in the second half" to "20-25 performers, about half of them below the age of 30, get one number each because there's no time for any more". Whether you want to call it a folk club if it's mostly whatever-you-feel-like is another question - if the common denominator is 'acoustic', maybe calling it an acoustic night would be simpler.