FPA is just that - a means of flying a fixed angle descent.
It's no different to VS in that if you are not on the correct profile for your, say 3deg, approach and select FPA 3degs then you will simply parallel the profile.
Also, if you ARE on the profile and, say, the machine ballons a bit as you select flap then it will NOT regain the profile but again will parallel it at your selected FPA.
I never used it, preferring VS which is less cumbersome to adjust because the increments are bigger.
What you are describing would be a VNAV profile where the AP would achieve specified points and angles between. On the 777s I flew this is not currently available due to software glitches.
Best way to fly a visual is by looking out the window and get your mate to call nominated check alts.