All white mulberrys are invasive in north america. Red mulberrys are native. The Illinois Everbearing Mulberry is a Morus Alba (white mulberry) x Morus Rubra (red mulberry) hybrid. Morus Rubra (Red Mulberry) is native, why not just plant that one instead? It produces fruit as well, and you have no invasive issues, as it's native across most of the eastern US. Red mulberry (Morus Rubra) is increasingly rare because of all these hybrids being made/sold/bought/planted and not invasive. The fruit is very similar. If you want a fruiting tree for family and animals, the native red will do you the same benefits as the hybrid you're asking about. Keep in mind, mulberry trees attract wildlife, specifically, racoons. If your area has a rabies problem, planting mulberry trees is probably not a good idea, as they will flock to your property for the fruit.

There's an old thread on this topic worth reading:
http://forums.gardenweb.com/forums/load/woodland/msg0717145310926.html

More info: http://www.na.fs.fed.us/pubs/silvics_manual/volume_2/morus/rubra.htm

Native info:
http://plants.usda.gov/core/profile?symbol=MORU2&mapType=nativity

About white mulberry's invasiness:
http://www.nature.org/ourinitiatives/regions/northamerica/unitedstates/indiana/journeywithnature/white-mulberry.xml
http://www.dcnr.state.pa.us/cs/groups/public/documents/document/dcnr_010306.pdf
http://www.invasive.org/browse/subinfo.cfm?sub=6050
http://www.na.fs.fed.us/fhp/invasive_plants/weeds/white_mulberry.pdf

Here's a link to the various hybrids (none of which I'd choose over the native red mulberry):
https://burntridgenursery.com/fruitingPlants/index_product.asp?dept=20&parent=7

Here's the factsheet for the red mulberry that's native to the area:
http://www.fs.fed.us/database/feis/plants/tree/morrub/all.html

I have one I planted 17 years ago. I love it. The fruit is delicious and it bears for a month or more every year.