Are 500cc to 510cc Breast Implants Too Big for 34 Full C?

In most instances this would take the average patient to larger cup size than a C cup. However, this is just an estimate. Sizers could help.

As Dr. Diaz said, none of us has seen you or examined you so it is hard to render any kind of judgment.
I would suggest you ask your surgeon to let you try a 500 cc implant in a bra with a tight t-shirt over it. That should give you a ballpark idea of the kind of total volume you will be carrying on your chest. If you love it, you are the one who will have to deal with it, so the rest of us should only offer advice as to wether its doable or not.
Given your skin envelope and nipple position certain techniques should make more sense than others. I will say that the breast tissue overlying the breast implant will be an issue. Sometimes patients with large breasts who get a large implant are bothered by the contrast in feel between the implant and the softer normal tissue, especially if with the effect of gravity it hangs below the implant.
Because of this sometimes it makes sense to remove some of your breast tissue and keep just enough to surround and envelope the implant but not overhang.
Dr. Edwards is right on the money when he says the larger the implant/breast combination the greater the likelihood of tweaking the surgical result down the line.
Check on the link below for some of the alternative skin excision patterns. I say this because the larger volume you add, the less skin you should have to remove.

It is always impossible for a surgeon to definitively know what size implant would be good without examining the patient. Since we have not, and cannot, examine you, anything we write are only general words of advice.
There are a few things we know for sure.
First, 500 cc is very big for anyone of any height. If you are currently a C cup size bra, this will make you more than a DD size cup.
Secondly, we know from pervious experience and studies which have been done, that once the implant is bigger than about 450 cc, the risk of complications down the road increases. Implants of that size weight a considerable amount. Human skin was not designed to hold that amount of weight. If you have 500 cc implants, it will stretch your breast skin very quickly. It will also thin out your existing breast tissue. If you get 500 cc implants, you will probably need another operation to lift your breasts again in a few years.
Lastly, implants of that size will be very obvious to anyone who sees you.
It is okay for you to have implants of that size put in, as long as you are aware of these above facts.