I haven't had experience with this plant, so I did some checking. Here's what a couple of invasive species experts had to say about Arundo Donax: "Arundo Donax is a well-known invasive in other parts of the country. Down south it behaves similarly to Phragmites in terms of aggressively occupying riparian areas. It is one of the top invaders in California primarily due to its ability to dominate wetlands and riparian corridors and because of its potential to spread via stem and rhizome fragments."
It appears we do not know yet how it would behave in Illinois. It may stay where it is planted, but there is also the possibility that it may aggressively spread.
"The risk of planting it and ‘seeing what happens’ would be that if it does start to spread, it is going to be very difficult to remove."
Both biologists said that they wouldn't plant it on their property. It is also known to reduce wildlife habitat, so I would not recommend planting it either. Here's what one had to say about the legality of planting it: "Legally, it is not a regulated plant in Illinois, so there are no restrictions for buying it."
Long story short, we don't recommend planting it, but if you do, watch it closely so if it starts to spread you can be on top of managing it before it gets out of control.
For more info. on invasive species check out: http://www.illinoisinvasives.org