How would you get a work permit and visa to work in the US? I think it would be pretty hard to do, esp just after graduating.
As to the masters degree vs MBA, I think the MBA carries more weight ESP with an internship, fixing more time to locate a job and get a professional network setup. However Illinois MBA is not really a top 10, 20 or even 40... Getting a job being an international applicant will have some bumps. Only about half of the grads had a job lined up at graduation. 80% 3 months after.
I would hate to pay full price for it. Would either try something higher rated or shoot for scholarship.
One crazy idea could be to get an MA that you got a scholarship for and then if you can't find a job, apply for an MBA and hopefully get into a better program or get a scholarship.