According to Wikipedia,
The electric potential energy of a system of point charges is defined as the work required to assemble this system of charges by bringing them close together, as in the system from an infinite distance.
This definition implies that an infinite distance is indeed traversable, but how is that even possible? What would an even entity need to traverse an infinite distance? Infinite time? Infinite velocity?
This is math.stackexchange, so everyone here read $$\textrm{"amount of work performed after traversing an infinite distance"}$$ as $$\textrm{"least upper bound on the amount of work performed when traversing an arbitrarily long distance"}$$ and went on with their lives.
If you want to worry more about this, you should probably take it to philosophy.stackexchange.