There is a defined recruiting path for advanced degree holders at MBB -- all three target JD/law postgrads in addition to PhDs and MDs. Check out each firm's website on recruiting advanced professional degree holders.
In the last couple of years, greater emphasis has been placed on diversifying the recruiting pool, but advanced degrees still make up only a small portion of the incoming class each year. Keep in mind that JD holders are placed in the same role as MBA grads (i.e. you all start off as an associate at McK or consultant at BCG/Bain).
Therefore, in summary to your questions:
- a law degree can lead to an interview, but offers are limited and the selection bar very high
- holding an undergrad degree from a non-target school is not a deal-breaker (you could still get an interview), but other applicants will have the right schools for both under- and post-grad
This all said, you should set realistic expectations about the probability of making it. By all means go for it, but also have a healthy balance of other consulting firms and career options in mind.
You shouldn't be investing a big chunk of your life picking up additional degrees solely for MBB ... do it because you would enjoy the experience and are happy with whatever door that opens for you down the road.