Issue on conditional PhD admission
I do not know what they will do in your case. However, in general, the procedure is such that when the application process for PhD happens, most students doing Bachelors or Masters degress in other countries are in their final year and do not have grades to send. However, if you do fail, then the offer of admission no longer stands, in general. 

For a PhD program, the minimum required standard is a bachelor's degree and if you fail that degree then why would they allow you entry? Having said that, now consider this. In certain countries, there are make-up exams for failed courses in a particular semester. If these make-up exams are taken before your offer of admission stands, i.e. Fall 2013 then you are good to enter. If not, then its bad luck for you. An offer of admission to a doctoral program only stands (in general) for that mentioned semester. You could potential defer the offer of admission another semester or year in order to take the make-up exams and then join the program. However, your chosen program may not allow this or may not have funds for you if you choose to join at a latter stage.

Basically, it all boils down to this. Contact the department immediately to ask for advice and tell them what options you have to finish your BS degree at home and whats the fastest route thats possible. Then see, what they have to say and take it from there. I speak from anecdotal evidence of a close friend who was forced to leave the offer of admission because he failed a couple of courses in his final year.

Do not try to fake your way through. I-20 or visa means nothing really for this problem and you will not be checked in general for proof of degree during your visa application process. But, be rest assured that you will be asked for proof of bachelor's degree once you join the program.