If the FPEB determines I'm still UNFIT can I appeal the ratings I've been offered?
Yes, absolutely. You're still entitled to a one-time VA Rating Reconsideration (VARR) once your proposed ratings come back from the VA. Happens all the time.
My thought is, how can a service member be truthful at VA C&P exams while still holding on to hope they'll be found FIT?
This one's an easy question and a very hard one at the same time. It's easy because the correct answer is "always tell the truth to your doctors, especially when it's for an official military purpose and lying could constitute a False Official Statement under UCMJ Article 107."
It's hard because I know you're struggling to be found Fit, and unvarnished honesty could get you found Unfit. To some extent, I think the degree to which you provide details to your C&P examiner is a matter for your own personal moral code. Don't lie, obviously, but there are details you may be able to ethically omit.
It's also a complicated question that you should talk to your attorney about. There are some details that will result in a higher rating but not increase your odds of being discharged (example: if you have a sleep apnea diagnosis, telling the doctor you use a CPAP will get you a whole bunch more money without materially increasing your chances of being kicked). And there are some details that will result in increased risk of an Unfit finding, but not get you a higher rating (example: if your knee hurts whenever you walk across uneven terrain, that probably doesn't increase your knee rating but it might make you non-deployable). So, talk with your attorney.
Additionally, do the FPEB make their decision while your at the board?
Depends entirely on your service branch. Navy side, the answer is usually no. In some cases, the Board will review your evidence before the hearing and decide to offer a "stipulation," meaning that they agree with what you're asking for and don't think we need to do the whole hearing. Then you'd know what the results were. But if you actually do the whole hearing, you'll have to wait at least a week to get your results back.