The FCC that I got when my cruise was cancelled did appear in my account. That FCC was available to use for anything cruise related, could be transferred, etc. When it is used, it is reflected as a payment on your statement.
The FCC for a price drop can only be used as an offset for cruise fare and cannot be transferred. Which is why, I would assume, that it has to be applied by a TA or NCL rep. When it is used, it is reflected as a discount (sometimes noted, sometimes not) against the cruise fare on your statement.
Just like there are different types of OBC, there are also different types of FCC and the rules are different. So yea, people may see FCC in their account. It depends on the source.