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If you were in a spaceship which was travelling at the same speed as the object you were looking at and it is emitting light in the visible spectrum, yes you will see it.
Galaxies will emit in the visible spectrum, but also in other wavelengths beyond the visible spectrum. It's the same with all celestial bodies - if you are looking at it and you're travelling at the same speed as it, you will see it as long as it emits in the visible spectrum.
What I was talking about before when I said "true colour" is this light it is emitting. The reason why as an observer a long way away probably won't see the true colour is because the expansion of the universe causes the objects to red-shift. Visible light then moves towards infrared and our eyes can't see that. So the "true colour" is correcting for this red-shift. If you're in a spaceship up close and moving at the same speed, you don't get the red-shift.
Sometimes astronomers will represent objects using false colour representation to demonstrate certain phenomena in a way that the layman can understand. If you would like an example of this, I would recommend googling "cartwheel galaxy xray vs visible". As your eye is unable to see x-rays, you would never be able to see the x-ray emissions from the cartwheel galaxy. To make it visible, you observe it with an x-ray telescope and then represent the x-rays as a visible colour.
I'm not sure I really understand what you're getting at, but you seem to be asking me if the human eye is capable of observing light in the visible spectrum? If you are asking me that question... then yes.