Remember, cohorts are simply an organizational unit. What distinguishes the Marian legions is that they were an entirely different structure, so I would not simply use cohorts to describe them. One, after all, does not use platoon as a synonym for modern infantry.
The reason the Romans only had a few provinces in those early days was that they were incapable of expanding. The legions could only be deployed during the campaigning season, afterwards, the soldiers had to go back to tend their farms. They did not have long enlistments and if they were offered, no one would have taken it. Even serving a few years away from home would mean ruin for a yeoman. There are numerous other reasons for the limited expansion until the ending years of the Republic, but this is the one that relates to the army.
Rameses: The Roman army and society as a whole was very different in 107 BCE than it was in 14 CE than it was in the 400s CE. Your question is akin to asking if the French armies under Napoleon could defeat Germany, why wouldn't those in World War II? The conditions, technology, and leadership were vastly different.