That's clearly untrue, since it's entirely possible to consider having perfectly sealed borders while not deporting undocumented immigrants. There is no way such a situation could be described as "open borders".
How would you have sealed borders with illegal immigrants? Where would they have come from? And if the border is sealed, why would they not be removed?
They would have arrived before the border was sealed. If you think anything short of retroactively applying restrictions is "open borders", we should discuss the colonization of America.