It would be a very realistic concern. Disease back then was probably the biggest killer of soldiers. The Romans were better than most in history for their hygiene, however approximately 5000 men per legion all living in close proximity and only having latrine pits, was ideal conditions for disease to spread.

On the food front, in the time of the Spartacus Rebellion Rome wasn't nearly at its peak, they didn't have Gaul or the Nile to be their breadbasket. This meant that most regions survived on their own growth and possibly some supplemented food from other provinces. The speed of the revolt meant that an army had to be mobilized fast which would mean there is no time to stockpile the vast amount of food you would need to keep a large force in the field.

If you couple this with the fact that Roman agriculture relied heavily on slave labour, when the slaves all downed tools and burned the estates, a lot of the crop yield in Italy would be lost.

Finally, moving onto the war consideration. Spartacus and his revolt was a huge horde of not only fighters but their wives, children and the old and infirm. They would eat just as much if not more than the Roman army following. Any food they would have would be collected from Roman estates and granaries. This kept them alive while at the same time deprived Roman armies of their own supplies. The general rule of thumb when being pursued by an enemy army in the field was to burn all crops and either kill or drive off the cattle to deprive these supplies to the enemy.

To wrap it all up, the high chance of disease in ancient armies coupled with tiring forced marches and a lack of supplies to keep their bodies strong. It is definitely feasible if not very likely that the Roman armies would have suffered disease and starvation to an extent.

I hope this helps :)