Yes, and that’s been a factor in several stories, either about ways to reduce the risk, or what happens when something hits a generation ship, causing irreparable damage. At some point, you’re going so fast, even interstellar gases can be a problem.
That said, space is a lot emptier than you think.
You wouldn’t even need to be going super fast for a crash into an asteroid to kill you.
From what I understand, space is mostly empty (in broad terms). Yes, there is the occasional Oumuamua, but no satellites to speak of - outside of the Voyager and Pioneer ships, and it’s debatable if they have left the solar system yet. You are extremely unlikely to run into any of the objects you mentioned.
Outer space is filled with gas, dust, a wind of charged particles from the stars, even photons. If you can manage to ramp up to even 20 percent of the speed of light, those things can become quite dangerous.
A dozen or so ships are launched at specifically staggered intervals so that they arrive at the destination planet in an orderly fashion, but because of wormholes, alien intervention, side trips or what have you, they all end up arriving at the exact same time. Then, to their considerable surprise, they discover the planet is already populated, because while all the ships were in transit, the people of their home planet mastered interstellar teleportation.
Does hilarity ensue?
No, penis.
Sorry, I had to. 
No need to apologize, I think this is coming together as a solid screenplay.