It depends on what your reference point is.
If no alkalinity was consumed, then yes, it would slowly creep up at a diminishing rate until it eventually matched the new water (it would take an infinite ammount of water changes to actually reach equalibrium (technically you would never actually reach equilibrium, but we can’t measure that low. Semantics, sorry)). You would fairly quickly hit a point where you couldn’t measure the difference between the tank water and new water.
If you are not dosing alkalinity and let it drop during the week, the water change will bring it back up higher than it would have with IO. Depending on how much is consumed, you may see larger swings between water changes. Without some alkalinity additions or periodic large water changes, you will see your alkalinity slowly decrease over time if waterchanges aren’t able to keep up with the alkalinity uptake.