Any of the 'stop leak' OTC stuff works by leaving a coating on surfaces. It's that buildup that stops the leaking fluid from getting by. Whether it's got more solids in it, or just heavy viscous compounds, either way that's how it works.
Anytime you introduce any product of that type you're going to coat all sorts of areas - including inside the passage tubes on the cooler. Its not some super scientific formula that exclusively bonds to a precise compound only present on a 30 year old seal but remaining inert in contact with every other surface.
So while you won't plug it solid, you will, potentially, do two things depending on exactly what's in the product you're using. 1) you decrease the passage size to some extend, however limited, and 2) you add a layer between the heat exchange surface and the fluid to be cooled.
Depending on how much build up you get from #1, and what the conduction properties are for the layer in #2, it's going to do something.
The oil cooler doesn't see the high pressures you'd get inside the internals so it's more prone to accretion in the slower moving areas.
And once that stuff is in a system, only way to get it out is replacement, recore, or boil it away.