At this point the date 2034 does not have any special significance for the Watchtower/JW religion. But it would not surprise me if JWs start speculating about 2034 in 15 or 20 years. Why is this?
Remember that Jesus said that his coming ("presence" in JW-speak) would be like the days of Noah (Matt. 24:37). The Watchtower teaches that Jesus' "presence" began in 1914. In Genesis 6:3, God said that man's days will be limited to 120 years. The Watchtower teaches that the flood came 120 years after God made this statement (see 12/15/2003 WT, p. 15, para. 6). Thus, it would not surprise me if the Watchtower starts hinting that the end could take place in 2034 (1914 + 120 = 2034).
Of course, if the Watchtower decides to go down this road, it will not do so for several years. The Watchtower tries to make its followers believe that the end is "imminent," and 2034 is not imminent by any standard. But, as 2034 gets closer it would not surprise me to see the Watchtower drop some hints in this respect.
If the Watchtower goes down this road, it will likely approach it they way it approached 1975. In the years leading up to 1975, the Watchtower was careful to avoid making any absolute predictions (apparently it learned from its 1914, 1918, and 1925 disasters). But, it published articles and books, and its representatives gave talks highlighting 1975 as an important year that holds many "possibilities." It would not surprise me if 2034 is treated similarly in the next 15 or 20 years. Time will tell.
And to those who think "this system" will be gone by 2034...I'm afraid you're going to be sorely disappointed (just like Russell, Rutherford, Knorr, Franz, and every other JW who was expecting the end in his/her lifetime). But, hey, don't say nobody ever told you!