Kind of but no. The frequincy of light would increase beyond visable light. As you speed up reds would turn orange then yellow then white and move to ultra Violet. Sound waves would start to have visible colour as they move up in spectrum until you are traveling so fast there is nothing but the slowest fluctuations that apear as light. Things that take centuries would be happening at frequincies higher than white light itself.

None of this would be possible though but let's say we could. One thing you could have on you ship would be a snap shot capture tool that took a sample shot of the radiation and produce a redshift back to some visible light showing a blurry image like a sudo slow motion camera but even still in the time your ships electrons travel micrometers decades would have passed it would only serve a purpose to ensure that earth still was there.