If you transfer between 2 wired PC it will not affect traffic going from a different wired pc or a difference PC connected via wireless. Obviously it could have some impact if one of the 2 end PC while it was transferring files also attempted to access the internet.
The switching part of the router in most device is using a completely different chip than the traffic going to the internet which is using the routing chip so they have little impact on either other. The wireless also runs on different chips so wired pc have no impact on the wireless users. Multiple wireless users do have a major impact on each other.