On the whole I'd say no. Most importantly, the "Marian reforms" were not the decisive game-changer we once thought. Rather, the 'reforms' were mainly the formalisation of already evident trends in Roman army recruitment, organisational and tactical practices. The enrollment of the capites censi in 107 BC was the central component of the 'reforms', but even this was just a capstone on a trend that had been increasing since the Second Punic War, formally severing a link between land ownership and military serve that had already ceased to exist (Gabba 12). The battlefield function of the Roman army did not change under Marius as far as I know: they were already using cohorts as their standard formation by this time (Keppie 63).

One thing that did change due to the Marian reforms was the standardisation of equipment and the official removal of the velites from the legions, though the replacement of the triarus' hasta with a sword so that all legionaries had similar equipment had already taken place (66). Marius also gets credit for the innovation with the pilum wherein the shaft bent or snapped so it could not be thrown back, though this was not really a game-changer (66). Marius' personal changes to his army during his years-long preparation for battle against the Cimbri and Teutones included the reduction in the numbers of camp-followers so that legionaries carried more equipment, hence 'Marius' mules', though this was something that numerous other generals had done in the past included Philip II of Macedon and Metellus Numidicus in Africa (66). Once again, while 'Marius' mules' stuck in the popular imagination it was not really a new thing. Generals had always retained and continued to retain after Marius great flexibility in how they trained and utilised their soldiers.

The loss of flexibility in the legions due to the gradual change from maniples to cohorts could potentially have had drawbacks (the Romans had done very well with the flexibility of maniples and flanking attacks against the Macedonians for instance), though the advantages of having much larger, stronger formations to manoevure was probably the better trade-off, especially against numerous hard-hitting enemies like the Gauls and Germans.This is just one of those things where there were no doubt drawbacks, but the pros probably outweighed the cons. Even so, the change from maniples to cohorts cannot be attributed to Marius anyway.

As such, I'd say that if anything really changed that affected Roman success between Arausio and Aquae Sextiae it was the fact that Gaius Marius was one of the greatest generals of all time and his predecessors against the Germans had been bunglers.

Sources:

Emilio Gabba, Republican Rome; The Army & The Allies, trans. PJ Cuff, Oxford: Basil Blackwell, 1973.

Lawrence Keppie, The Making of the Roman Army; From Republic to Empire, Norman: University of Oklahoma Press, 1998 (1984)