This is what I believe that this particular Scripture is saying; that not only do the saints long to be united with Christ in the marriage supper of the Lamb, but so does the Spirit.
I think that just as Christ yearned to be with the Father during Jesus' time on earth, in that He felt homesick and out of place, I think the same is true for the believer, but also the Holy Spirit. I think that the Spirit is yearning, and homesick to return home to be with Jesus. Jesus ascended, and the Holy Spirit descended.
So it makes since to me, in that we are partakers of the Holy Ghost, and that He lives in us (Christ in you, the hope of glory) that we that are alive, and the Spirit within us want Jesus to return, so both the Spirit (the Holy Ghost) and the bride (the church) say, come (come and take us home, Lord Jesus).