[echelon]

Would it be "accidental" if they were traveling in a direct vector approaching us?

Incredibly implausible idea for the sheer improbability, but fun to imagine nevertheless.

[erelde]

I would think that by the time they actually move some meaningful distance, their sun would not be 'behind' them anymore, they'd still be moving toward ours, but as the whole thing is constantly moving, their sun would have moved relative to ours.