yes you can you just gotta do it backwards.
in the sequence edit window set it to "move" and set the time on the left hand side later by how many ticks you want it to be earlier. so if you wanted the track to be shifted 5 ticks earlier you would set the time (on the left hand side) to 001.01.05 and leave the start time (on the right) set to 001.01.00. then when you hit "do it" the everything on the track from 001.01.05 will be shifted to 001.01.00.
not the greatest method in the world but it works.
peace.