Your current cassette has smallest cog of what, 11? 12? 13? The RD is presumably able to take up slack on that cog, so it will also be able to do it with a road cassette which will have probably an 11 smallest/fastest cog.
Your limiter on a mtb though would be that you could spin out in the top gear because your mtb chainrings are smaller than typical road chainrings.
If you replace the mtb cassette with a road cassette, that will not buy you more speed, all it will do is exchange climbing ability for close gearing, i.e. your gear range would get compressed towards the top of what you already have.
If you want to go fast on a mtb, as recommended above,
#1 criteria is to make sure you have tires that are smooth enough in the center profile that you can roll fast on asphalt.