Yeah if the A-H 2nd army stays and participates in the offensive Serbia is in serious trouble; having to deal with an extra 4 corps and 1 cavalry division attacking across the Danube isn't going to enable the Serbs to counterattack the A-H 5th and 6th armies on the Dvina and Sava.If Russia doesn't mobilise, Germany will not mobilise either. WW1 as we know it will not happen. There may be a 3rd Balkans War, where the Austro-Hungarians demonstrate that they are unable to defeat the Serbs, which in turn may lead to the disintegration of the Austro-Hungarian Empire, which in turn may lead to a European war for the spoils.
The 2nd army was to attack across the Danube, the 5th Army across the Sava, and the 6th over the Drina. If the Serbs opt to fight on the Danube they are letting the 6th army take them in the flank, though terrain will be a major problem. Also the Austrians had a lot more firepower than the Serbs and a lot more ammo; the Serbs thought they would need 10 years to rebuild munition stocks after the last Balkan war and indeed they ran out pretty quickly and had to go hand to mouth from their 1 shell production facility by Autumn.THeOTL attack came in the most favorable territory for the defender - the original plan called for an attack over the Danube and from North to SOuth (instead West to East from Bosnia). - THE AH army might not make a glorous run, but in the long run the lessons learned will be invaluable.
But the real lesson learned would be one learned by the Slavic nations - that is despite rhetoric the Russinas are NOT interested in saving their slavic brethren. Imagine what consequences for the Slavic nations within the Monarchy