There are all sorts of possible outcomes, the warping of space by the FS drive may counter-act the red/blue-shift, it may increase it, it may lens all real light around you, so that you would end up seeing nothing, or a tiny little blue-white dot in the centre of your view.
Any time-dialation effects would be minimal on the system scale; sitting at <1C at the host star, looking at a planet 1000ls away, you would see it's orbital position 1000 seconds ago. Travelling towards it at 1C+ you would see it approach its actual position as you approached it. However, the distance an average planetary body moves in a thousand seconds is negligible.
Time-dialation effects would be most apparent if you flew away into the furthest reaches of a solar-system, orientated yourself so that the disc was face-on ( orbits were circles on your screen ) then, from light-months out, hurtled towards the system at high super-luminal speeds ( light-days a second ), you would then probably notice the time-accelleration effects of the fasted orbiting bodies.
I would like some more 'tells' that you were travelling FTL but the game is great as is and time-dialation wouldn't make much difference.
PS: Time-dialation would be apparent if a Nova or something travelling at 1C could be viewed, overtaken and then viewed again from 30ls away or something ( that would be neat ).