Can the Economy function without Unskilled Labor?

Yes, it needs a certain amount of it. In the US, at least, that proportion of the work force goes down all the time, though. Keep in mind that just about everyone who today holds a job that you would consider highly skilled, at one point held one of those unskilled "lowest" jobs. I know I did. Those jobs are essential to give people job experience on which to build. The vast majority of people earning minimum wage today will not be in those jobs five years from now.