Honestly, I'm afraid even a TINY ship won't fair well against interstellar dust at 20% light speed!
Let alone a massive human sized ship! Wish I could say otherwise... but...
Since you and I's debate here is certainly fun and interesting and stimulating (and because it's been a few years since I myself did the calculations, and was a bit dismayed) I went ahead and fired up "The Old Google"!
Found things like this even with velocities at around 20% light speed:
"We calculated the energy that each interstellar atom or dust grain transfers to the ship along the path of the projectile in the ship. This acquired energy rapidly heats a spot on the ship surface to high temperature, resulting in damage by reducing the material strength, melting or evaporation."
Another quote from that article:
"Any spacecraft traveling at 20% the speed of light (0.2 c) could easily be damaged or destroyed if it suffered a collision with even the tiniest of this particulate matter."
Getting back to FTL however, that for now is the fringe domain of physics, that's still closer to "magic" than true understanding!
But ya, indeed, FTL would have to "magically" get to that speed by cheating somehow. (Maybe it would tap the energy of the multiverse of hyperspace to do it, or not need to tap energy, etc...)
But once at that speed, and travelling within our space-time, it's very reasonable (and I would argue HIGHLY likely) that the energy of impact would still be determined by the relative speeds between the 2 objects.
Interestingly:
While on a local level, the Universe seems to pretty much follow the law of Conservation of Energy, it does not do so on Cosmic levels!
So cosmically you can gain energy from nothing (dark energy for example), and so perhaps a more cosmic or unknown source of energy would be the energy translated, when the ship impacts a fleck of dust.
Of course, some forms of fantasy-FTL try to get around that by entering a "hyper space realm", and sailing there instead!
Which who knows, might be feasible? We know quantum entanglement operates partially faster than light, but we don't know the conduit of that. Maybe we could say that conduit is "hyper space" (or the fabric of space-time itself, rather than the "interior" of space-time).
So ya, sure maybe you could travel there, and never worry about hitting anything! Although even then, seems like you might run into quantum-entanglement "information" in that realm, if that's what is being used!?
But all of this is starting to sound like nonsense and highly fringe!
And of course, once you are flung out of hyperspace and back into space-time you could still have some insane velocity... perhaps?!
I could see your forward shield just simply EXPLODING into a kind of beautiful shower of insane blue glow and sparks the moment you exit hyperspace, and come slamming and screaming back into regular space-time!
Still yet other forms of FTL involve forming a warp bubble and bending/folding space, but that has some possible issues too involving energies exchanged between your sailing bubble, and even a fleck of matter along the way.
Anyways, better stop there!