Shakespeare does seem to wish us to think that fate had a lot to do with Romeo and Juliet's tragic end. He calls them "star-crossed lovers" in the prologue and has Romeo misgiving "some fearful consequence hanging in the stars" which is all going to happen because he crashed Capulet's party. Romeo also calls himself "Fortune's Fool".
This is all very well, but Romeo is fortune's fool because he allowed himself to lose control and give in to his feelings of guilt and anger. Indeed a great deal of what happens is due to circumstances very much in the control of Romeo and Juliet.
There is one overwhelming piece of bad luck over which nobody had any control--the fact that Friar John would be unable to deliver his message to Romeo, so that Romeo would be unable to rescue Juliet from the tomb and take her to Mantua with him. Of course if we consider as a part of the story the idea that Capulet decided Tuesday night to move the wedding from Thursday to Wednesday morning, Friar John's message would have been no good even if it had arrived. The aplomb with which Juliet and the friar accept this changed wedding date and thus a change in their carefully worked out timetable (to say nothing of the failure of anyone to worry about all those wedding guests who are going to show up on Thursday a day late) makes the whole "change of the wedding date" episode so incredible that it is frequently cut from performances of the play.