The wikia page says nothing about this. I remember from my first playthrough that nothing happens if I let him inspect the ship in terms of later repercussions. I never tried sending him away though.
Will it have some impact on the story later?
When I did this I prevented him from inspecting my ship. Other than that the only effects on the game is reputation, as described in your linked article.
Only 2 Renegade points can be gained from this mission, whether you completely refuse to allow the Admiral his inspection tour, or allow it and then take all possible Renegade conversation options. You will gain 2 Paragon points by allowing the Admiral to inspect the ship and taking every possible Paragon conversation option.