UIUC Undergraduate Mechanical Engineering Job recruitment and graduate school placement.

I am wondering what type of companies, and specifically what companies, recruit UIUC Undergraduate Mechanical Engineers.

I am interested in management consulting but want a mechanical engineering degree.
Does Mckinsey, BCG and Bain recruit Mechanical Engineers out of undergrad.
Does Deloitte, Accenture, and PwC recruit MechEs out of undergrad.

Does Microsoft, Boeing, GE, etc recruit mechanical engineers?

Is there a strong chance for me to be able to get a Business Analyst position at a top consulting firm out of UIUC Engineering?

Also, what schools do UIUC Engineers go on to do there graduate studies go to.

Do UIUC Engineers get into top MBA programs such as Harvard, Penn, Booth, Stern, McCormick, etc.?

Thank You