The answer is a simple "No.". Don't allow them. The vast majority will fail to meet reasonable criteria for acceptance, which is enough of a reason to reject them. For the rest, even if they're acceptable in terms of quality, the sheer cost of reviewing every pull request in detail and sorting the minority of acceptable requests from the swamp of slop will itself damage the project, diverting maintainer time away from feature work and fixing bugs, badly enough that it's not worth it. I think this sums it up nicely:
Why should I spend my time reading something you didn't care enough about to spend time writing?