Will 371 cc's give me a C cup or larger?

Thank you for the question.  There is no accurate/reliable/predictable correlation between size/profile breast implant utilized and cup size achieved. Despite your good description of goals, online consultants will not be able to provide you with specific enough advice to be truly helpful. Ultimately, careful communication of your goals (in my practice I prefer the use of goal pictures, direct examination/communication in front of a full-length mirror, and computer imaging) will be critical. Given that your surgery is coming up, I would suggest that you schedule additional time to spend with your plastic surgeon communicating your goals, preferably prior to the date of surgery.
Generally speaking, the best online advice I can give to ladies who are considering  breast augmentation surgery ( regarding breast implant size/profile selection) is:
1. Concentrate on choosing your plastic surgeon carefully.  Concentrate on appropriate training, certification, and the ability of the plastic surgeon to achieve the results you are looking for. Ask to see lots of examples of his/her work.
2. Have a full discussion and communication regarding your desired goals  with your plastic surgeon. This communication will be critical in determining  breast implant size/type/profile will most likely help achieve your goals. 
In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. I have found that the use of words such as  “natural” or "C cup” or "big and fake" etc means different things to different people and therefore prove unhelpful.
 Also, as you know, cup size varies depending on him who makes the bra; therefore, discussing desired cup  size may also be inaccurate.  Again, the use of computer imaging has been very helpful during the communication process, in our practice.
3.  Once you feel you have communicated your goals clearly,  allow your plastic surgeon to use his/her years of experience/judgment to choose the breast implant size/profile that will best meet your goals.  Again, in my practice, this decision is usually made during surgery,  after the use of temporary intraoperative sizers.
I hope this (and the attached link, dedicated to breast  augmentation surgery concerns) helps. Best wishes. 

The best cosmetic result in any particular breast
augmentation patient depends on a variety of factors, including: Your
individual anatomy, realistic expectations, a thorough discussion with the
plastic surgeon about the options, and an understanding of the pros and cons of
any particular implant choice. Proper sizing is not just about the number of
cc’s. The thickness of your tissue, breast dimensions which include the width,
height, and projection, as well as chest wall width all need to be considered
when choosing an implant. Trying on implant “sizers” of various shapes and
volumes while wearing a tight t-shirt, bra, or bathing sit at a preoperative
visit will help you and your surgeon choose the optimal implant.

There are no manufacturers' standards for cup sizing in the bra industry. The
cups of a 34 C and a 38 C are significantly different. Cup size varies from
manufacturer to manufacturer and even within styles from any particular
manufacturer.

Keep in mind that following the advice from a surgeon on this or any other
website who proposes to tell you exactly what to do without examining you,
physically feeling the tissue, assessing your desired outcome, taking a full
medical history, and discussing the pros and cons of each operative procedure
would not be in your best interest. I would suggest that yourplastic surgeon be certified by the American Board of Plastic Surgery and ideally a member of the
American Society for Aesthetic Plastic Surgery (ASAPS) that you trust and are
comfortable with. You should discuss your concerns with that surgeon in person.

Robert Singer, MD FACS

La Jolla, California

In terms of picking the right implants to achieve your goals, generally speaking, I consider two
factors when selecting implants for my patients:1. Dimensional planning2. Gel Implant Sizing systemDimensional
planning – The measurements of your chest wall are taken. Also, the
breast dimensions including the height, width, and current dimensions of
each breast form the basis of dimensional planning. Based on these
measurements, the implant size is recommended. This will give you a
unique breast implant that is suited for your body frame. However, there
are some limitations of what size we can recommend. For instance, some
implants may just be too big for a narrow chest wall. Your surgeon can
review this with you during the consultation.Gel Implant Sizing
system – During the preliminary breast implant consultation, you will
be provided with an option to “try on” a variety of implant shapes and
sizes. You can also visualize the possible outcomes of your surgery
which helps you to get that perfect size to give you the shape that you
longed for. This way your preferences are known and you can then pick a
range of implants that will “fit” just right to give a soft natural
fuller look. Hope this helps.Dr.BasuHouston, TX