In short...no.
If not Franz Ferdinand, then some other (relatively important) Austrian official will die in some assassination attempt in the months or year following. You see, the Archduke's assassination was not an isolated incident, and between 1900 and 1914 there were dozens of assassinations and attempted assassinations of various officials, including Serbian officials that leaned towards Austria, as well as Austrian officials in various posts by Serb and Slavic nationalists that hated Austrian meddling in the Balkans.
Now, if you want the plot to try but fail (that is, no wrong turn for the driver/the captain standing on the correct running board when the driver realises his mistake and they come across the sandwich-eating Princep...), I think the mere attempt on the Archduke's life is enough to still set the powder keg alight in the Balkans. Austria will still demand an investigation, and while it may not meddle with the Serbian investigation, unless the findings from Belgrade match up with what Austria wants to hear, we'll have war. Maybe delayed by a few months, but war all the same.
Oh, and if both the Archduke and the General are hit (Sophie's bullet 'missed', aimed supposedly for the general, the name of whom I've forgotten), instead of 5 weeks till war, expect Europe to go up in 2-3 weeks time.