Depends entirely on how the FTL works and how the sensors work. For example, if the long range sensors operate through hyperspace or something like that, it's plausible that you're capable of detecting ships that are moving through hyperspace at incredible ranges yet be unable to detect anything in real-space except by bouncing light off it. Conversely it might be the case that it's magic trek sensors that can see everything at implausible range through unexplained mechanisms (except when the strange mineral of the week is blocking sensors).
You argue that you can maneuver around missiles and such, but it once again depends on the situation. Suppose I launch a spread pattern of 7 missiles, one aimed based on your current trajectory and the other six steering outwards at various angles anticipating where you could potentially maneuver to. There is no such thing as "range" on these missiles, just delta-V, they can just cruise towards you for a month if necessary and only activate their engines in response to your changing momentum when you do burns to maneuver. Outrunning the missiles consists of extending beyond their own capacity to burn by cancelling out their momentum relative to you, matching their speed and trajectory such that they will never hit you. They keep accelerating, so you have to keep accelerating the same direction. This is possible, but you have now conceded the battlefield. If you were defending your home-world it's now a pile of radioactive debris because you had to outrun my missiles.
I could launch my payload in waves of missiles at light-second intervals away and keep a portion in reserve. I could chase you down and keep firing, my own engines matching YOUR engines, and if I can run you out of Delta-V, you won't be able to run away anymore and I can fire my reserve. Luckily for you, we now enter the point defense phase of things, where you use your laser that you were hoping to kill me with to intercept the incoming missiles. Can you do it in time? We don't know, find out on the next exciting episode of Boy I Wish I Didn't Care About Realism Because this is Boring. In any case though, you've now been neutralized as a threat if you can no-longer pursue me because you have to outrun my missiles and I've returned to base to seek resupply. A long slog, a battle of maneuver and positioning the results of which could probably be optimally calculated by a computer program.
The wrinkle comes when we get FTL and exotic drives though. In these games it's simplified as being a battle takes place whenever my guys run into your guys on the game map. This might imply that combat is taking place at FTL speeds, or that FTL is periodically de-activated over long journeys, at which point fighting can occur in real-space at normal velocities. If I can use magical impulse drive (like Trek) to attain huge sublight speeds, then can't I also make impulse missiles? And if combat is taking place at FTL, can I use "warp sustainer" type things to make my missiles also fire at FTL? Or if it's like alternate hyperspace dimension the rules could be bloody anything I please. It's impossible to answer without a firm grounding in the lore and GalCiv lore is an inconsistent, throw-everything-in-at-once type of deal that rarely goes into any detail. Since it's an abstract game we don't actually see detailed realistic combat going on - the battleviewer is pretty laughable with everyone firing at ludicrously close ranges and stuff.