Breast reduction from 34DD. Would this leave me smaller than a B cup?

At size 34, each 100 grams removed corresponds to 1 cup size change.  400 gram removal would take you down to a A or B.  Unfortunately, you have not provided photographs.  The technique I recommend is The Bellesoma Method.  This will reduce and reshape your breast tissue creating upper pole fullness without implants, elevate them higher on the chest wall and more medial to increase your cleavage.  The weight of the breast is transferred to the underlying pectoralis major muscle resulting in pain relief and long term stability.  Vertical scars are avoided, nipple sensation and the ability to breast feed are maintained.Best Wishes,Gary Horndeski, M.D.

It is difficult to use cup sizes because they are not standardized. Good communication with your surgeon is necessary and I would return for visit for a discussion. Also ask whether the same surgeon will be performing the operation on both sides of the body or if there is a assistant surgeon doing the surgery on one breast.

I would focus primarily on your desired result, not chasing a number that the insurance company dictates.  You may end up too small and be unhappy.  Usually in a breast reduction about half the tissue is removed along with a lot of skin.  Cup size is hard to predict but most patients go down 2-3 cup sizes when they have a reduction.  It is best to decide what your best aesthetic result would be first!

Thank you for the question.
There is no direct correlation between the amount of tissue removed and the ultimate cup size that a patient will wear after breast reduction surgery.  There is simply too much variability among bra cup manufactures to make it a useful metric when it comes to preoperative communication and/or post operative predictions.For example, I do not think that the generalizations of "200 cc equates to 1 cup" hold any validity or are helpful in any specific or practical way.  In my practice, I ask patients not to communicate their goals, or evaluate the outcome of the procedure performed, based on cup size references.
 Before undergoing the breast reduction procedure it will be very important to communicate your size goals with your surgeon (who you should choose very carefully). Most patients wish to achieve enough of a reduction to help with their symptoms while remaining proportionate with the remainder of their torso. 
With the goal of improving communication with my patients I find the use of photographs of “goal” pictures (and breasts that are too big or too small) very helpful. For example, I have found that the use of words such as “natural” or “B or C cup” means different things to different people and therefore prove unhelpful. Again, cup size varies depending on who makes the bra; therefore, discussing desired cup size may also be inaccurate. 
Once you have communicated your goals carefully, your plastic surgeon will be able to provide you with an estimation of how much tissue will need to be removed, in order to achieve your desired outcome.
Best wishes with your breast reduction procedure; hopefully you will be very pleased with the outcome of the procedure performed.