Obviously an MPH won't really have a ton of impact with any deficiencies in biomedical science core classes you have already taken or need to take. Your GPA is low but not unreasonable for a bioengineering major, but you want to find some schools that may have a favorable experience taking applicants with similar stats as yours. There is also University of Illinois's Carle School of Medicine that likes to promote itself as engineering-friendly but it's newer... but worth reaching out about your chances. That said, no doubt the pedigree of going to Yale MPH or UNC MPH might help you with connections within each school. I've known a lot of aspiring premeds go to Yale for an MPH and decide to go more MPH than MD. Nothing wrong with that, and they're doing very well.
ADDED: It does depend a lot on your MCAT score, so let us know how that goes.