Odds of landing a job alone, being an international student depends on your proactiveness, networking skills, alumni connections, and various other economy related factors. Oh yea, how well you do in your program is also an importnat factor though.
And regarding stratetigic consulting job, do you have experience in IT consulting? If yes, it would be easier for you. If you are just a software developer, then you would be among the same pool of job applicants, who are just willing to do anything for a strategic consulting role.
Best,
Bharadwaj