Not at light years. How many non-binary stars do we see colliding with other stars. They don’t. Even when andromeda runs into the Milky Way it won’t result in stars colliding. The chance of the sun colliding with another sun is somewhere in the 10^30 range.
Voyager may end up in a solar system briefly as a high speed extra solar object like Oumuamua, but the chance of it being close enough to suffer any physical affect would be small - think how small a target that would be and how rare stars are. To get within 1 light day would mean passing 100,000 stars within one light year. To get down to earth distance is something like 4 billion passes within a 1 light year distance.
Now sure predicting the future beyond say 100 billion years is tricky, and not something you could simulate, but for all intents and purposes the voyagers will continue long after Earth has died. It (and other craft on escape trajectories like new horizons and pioneers) will be the last remnants of human civilisation