You can technically, but that would be a bad idea. C-II prescriptions are very tightly controlled. You don't have the 6 months to fill like you do with C-III - C-V. I think you have from 7-30days to get it filled. There are no refills allowed and refills cannot be called in so you'd have to mail the precription immediately each time, then wait for it to be verified, then wait for it to be filled, then wait for delivery.
I know from have a few C-II's in my time that getting a legit C-II filled can be a hassle. The pharmacies are scared to death of filling incorrectly or filling a fake prescription that many times they will not fill at night because they need to call the doc to verify. I can see no upside to mailing a C-II in to be filled. If it is for plain oxycodone/tylenol (Percocet), the generic is cheap enough that there's little use in shopping for a good price. If it is for Oxy-cotin, that is another deal. Those prices are very high, as they are still under patent. You may want to shop for a price, but via mailorder is again not an option as oxycotin is generally reserved for chronic pain, meaning multiple prescriptions each year (at least 12) as they are written for no more than 30 days with zero refills and that could put you in dire straits if you run out and shipping is delayed.

Stick to the local pharmacy for that one, but you can call pharmacies for prices, they are usually happy to let you know what the price is expected to be.

Farmer