As the title suggests... If there is by any chance any correlation it would be a huge NO U moment from the Serbs. But my hopes are low... Thanks in advance for any answers!!
28th June in Gregorian calendar is also 15th June in Julian Calendar which is the so-called Vidovdan - Saint Vitus Day - important holiday especially for Serbs and the Serbian Orthodox Church and an anniversary of the Battle on Kosovo Field which took place in 1389.
Sadly I am afraid that all of this is just a coincidence.
Franz Ferdinand's visit to Sarajevo was scheduled to happen right after the completion of military manuevers by the XV and XVI Imperial and Royal Army Corps. However the precise duration of these manuevers could not be predicted in advance as they depended on numerous factors, eg. weather conditions or how well the manuevers are conducted which in itself depended on the training of the troops in question. It just so happened that that day was Sunday 28th June 1914.
The assassins logically could not have chosen the date themselves as it all depended on which day Franz Ferdinand would arrive. They were determined to assassinate him since March 1914 when newspapers first mentioned that Franz Ferdinand would visit Bosnia but without giving any specific date.
Source: RAUCHENSTEINER, Manfried, The First World War and the End of the Habsburg Monarchy, 1914 – 1918, 2015