Where I went to undergrad, the grad students had to take entrance exams, and if they didn't pass in a particular subject, the had to take the undergrad level class in the same subject (e.g., organic chem.) but they had to take an honors section if it was offered. Based on that, I would say the entrance exams are probably comparable to the final exam in one of the honors level classes.
Cumes vary a lot from place to place. I have heard of cumes that were reasonably easy and some that were impossibly difficult. It seems to be very dependent on which professor writes the cume.
My undergrad degree isn't ACS accredited and it hasn't held me back any. Do people really think that this accredidation is that important?
By the way g c, most of the staff here is made up of grad students around the US, with a couple from overseas. Some staff are finishing up their undergrad. There are a few people floating around who have completed their PhDs as well.