Yes, you can. If I expected you to take two hours to finish your homework and you did it in forty minutes, I would say to you 'Have you finished your homework already?'. I know that you seem to have finished it, and I am surprised that it took you so little time. This is very different from 'Have you finished your homework yet?', when I am enquiring whether you have finished or not.

Have you finished it yet? (speaker doesn't know, no expectations) Have you finished it already? (speaker is looking at finished homework, it's done)