I'm no medical expert, but I don't know why it would be dangerous just to go into labour whilst transverse, unless there are other issues. Simply, you just won't progress and you'll need a c/s if the baby doesn't turn. I believe that labour can actually turn some transverse babies - this was certainly the case with my dd2 who was transverse the day I went into labour with her.

If you have an appt, ask the obstetrician exactly what the danger is if you are allowed to go to term regardless of the baby's position.