Absolutely.
For expedited visas, when you need to be here on an urgent basis, almost all people would be willing to pay extra, as they do for passports when they need a passport overnight. We now have a passport service. We don't have to call our MP, as we used to have to 10 years ago, to get a passport in 24 hours. We pay extra for it, and people do it gladly.
I think overwhelmingly people would pay for that expedited service.